Arrest and kill all the crew as soon as the ship makes port

It's already too late.

As soon as that ship made port the sailors made for the nearest bar, brothel or other place of negotiable affection and consumption of alcohol. The whole town already knows. Many of them probably knew before you did. Ships have already left port on the turning tide with that knowledge before you knew.

The problem isn't about preventing the neighbouring kingdoms from finding out, it's about how long you've got to act before they decide to take a look for themselves.

This is an X/Y question: the stated goal is

What I would like is to make profit out of this new continent - alone.

so the question you should have asked is

How can I ensure that?

The answer is not to prevent other people finding out about its existence, but to give them a strong disincentive to compete with you. If you look at the history of European exploitation of the Americas after Columbus, there are a series of Papal bulls about who can claim land where. The details are a bit complicated (see Wikipedia:Treaty of Tordesillas), but the concept can work for you if you adopt the scenario of a powerful supranational authority, probably religious, which gets involved in politics but not in the hassle of running colonies and trading posts. Maybe make some concessions on existing intracontinental trade to sweeten things for your neighbours.

Naval Technology Isn't Very Advanced

Ships that can handle open waters and rough seas just aren't something that has been made before. Up until now ships navigated primarily utilizing the coasts and were never really out of sight of land for more than a few days at a time. Frankly, it was a miracle the foolhardy captain who took his vessel across open water even managed to make the trip! It is unlikely that without a revolution in shipbuilding technology that trade could be conducted. Why would anyone go through all the expense? All the profitable trade routes are close by and easy to get to, why bother building bigger tougher more stable ships when you can already make a ton of money just following the coasts and sticking to the shallower calmer waters?

It Was a Rough Voyage

Unfortunately very few of the sailors even survived the journey. In History it was not uncommon for expeditions to set sail with many ships and hundreds of sailors only to return with one ragged and battered boat with only a dozen scurvy ridden and starving survivors. Or just to never return at all... Unfortunately none from the ill fated voyage survived except a few diseased and sickly men who sadly died ranting about nonsense and fever dreams (You just kind of hide the fact that they all died from acute knife to the throat syndrome.) Very big tragedy, their widows and orphans will be compensated!

Quietly Build a Fleet Of Capable Ships

Navy? What navy? These are fishing vessels! We hear that in the great oceans to the west there might be untapped fisheries and we need lots of ships to catch them! Why would anyone need a navy? Certainly not our kingdom of humble fishermen!

Lay Claim to all New Land's

Once you have established a beach head and adequately oppressed all the natives with your diseases and built up a really good network of forts and outposts you simply declare that it is all yours and anyone who messes with it can expect to engage in warfare with you. Thanks to all of the profits you have leveraged from the continent while everyone else are a decade behind in figuring out how deep water navies work you have built up a very sizable army and navy. Will your uncontested claim to the continent remain so? Probably not, but you can very much ensure that doing so remains extremely costly, and prolong your monopoly. Even once competition starts up you have such a leg up that its still massively profitable.

Total Secrecy is Unlikely

To expect nobody to ever find out is not possible. Sailors talk. Sailors talk a lot. when they start telling tales of piles of gold, mountains of new exotic spices, and lands populated by exotic bare chested women somebody is going to be ahem intrigued enough to go check it out. Huge campaigns of colonization and exploitation arose from superstitious and wide eyed tall tales about cities of tall bare chested female warriors, fountains that cured aging, cities of gold, and assorted other fantastical tripe. Plus, somebody is going to notice the exotic and heretofore unseen goods that are suddenly making you rich. If one of a curious nature visits the port-side tavern and buys ol' Jenkins there a few pints he'll tell ya all about where they came from, and how his lousy no good greedy captain had him flogged and didn't even pay him enough for a good slug of rum while getting his own pockets fat himself, the greedy bastard!. (If there's one thing sailors do more than tell tall tales its drunkenly bitch about their officers to strangers.)

Point being, there's no way to expect full secrecy, one can simply utilize the head start they've been given.

Map secrecy

Hiding real location of new areas was common. For example, Columbus wrote a public report which "say much and reveal nothing", no coordinates, bearings etc. Only several people on a ship knew navigation. Others have no time for observations nor education to track the way and understand where they were.

During the Age of Discovery there were navigation issues so maps were inaccurate. This is a reason why Columbus mixed India and America: it's hard to calculate how far to the west you travel. That's why detailed ship's log was so important: just coordinates was insufficient. Few people had access to the ship's log.

So to prevent leaks about precise location all you need is to make sure captains and some officers are faithful.

Needless in same route

Columbus was going west looking path to India because old routes was long and somewhat monopolised. After his discovery, others went west for the same reason. It took some years to realize that New World was discovered.

So if nobody is interested in an alternative way to the East, other states don't want to spy on what are you found and repeat this expedition. This provide little delay since after your kingdom received (exotic and expensive) goods, rivals would want to know where and how you get them.

Getting rich from colony

Colonies are found to get resources from them. Discovering new continent would lead to abruptly increasing treasure of your kingdom. This is goal for colony and most decisive indicator that you found something important.

Another indicator is exotic goods. Only exotic plants and animals could say you that a new continent found. And they said about New World for all smart people who see them.

If you don't use new continent then you probably could hide the discovering for some years. But what the point if you don't use it?

Not for long once you try to make advantage of the new continent.

The thing is: Simply knowing that there is a new continent does not give you any advantage. You need to use the new continent. And this means you either import goods from the continent which are either much cheaper or completely unknown, warning everyone that you have access to new resources. Or even if you do not import goods, just using new ports to dominate or discover new sea routes gives hints to competitors. Suspiciously long absent ships or rumors from seamen will warn the other countries that you have discovered something.

Failed strategies from the outset:

Total secrecy.

You need ships and seamen to have access to the new continent. Those voyages must be planned and equipped. There are so many people involved that the secret will be exposed. The example of the Vikings is not convincing because the Vikings were essentially pirates and they did not exploit the new continent.

The other people are warmongering child-eaters.

You could try to paint the other countries as dangerous adversaries. If they in fact are and dumb enough to raid a city the first time they encounter the new continent, then your argument has merit. The problem is: The natives are not dumb. They can deduce that it is in your interest to be the single trading partner. First they will be curious who those other people are and if they encounter them the first time, you can expect that they treat them cautiously, but friendly and ask them what they know about your country. The "Shogun" from Clavell is in effect the true story of William Adams who informed the Japanese authorities that their "friends", the Portuguese, have signed the Treaty of Tordesillas/Treaty of Zaragoza
which said that Japan was Portuguese "property" coincidentally without informing Japan.

Best strategy:

Keep the others out by being the most powerful sea nation. Wait until you have established a power base on the new continent, exploit the new discovery and use the winnings to strengthen your hold. Attack any intruder mercilessly and/or force convince the other nations to a treaty which singles you out as trading partner.

To summarize your situation: You stumbled upon a pot of gold in a place where other have found nothing, even when they searched. Good for you!

But here is the problem, as you already know: How to hide the metaphorical pot of gold? With alot of trade going on it would be strange for others if your kingdom suddenly has more ressources than you should naturally have.

As soon as this thought crops up in the mind of your trade partners/ rivals/ neighbours, they want to know how and where you got that stuff. They will send spies and agents to learn what is behind that secret.

The question now is not if, but when the others get to know from your discovery. You should plan accordingly:

First, execute the crew of that ship. Keep the captain and the officers alive, but under arrest. Sailors talk to much when drunk. You could excuse all that with some kind of strange sickness, e.g. Black Death or your worlds equivalent.

Second, force your prisoners to exactly describe what they found, and let them draw maps.

Third, build secret shipyards and harbours, and build a small and secret fleet. Build all that on the coast, far away from cities and villages. Make the workers there understand, that every bit of information they leak would be very detriemental to their health...

Last, but not least: Build a few well defendet outpost on that new continent, and scout it. Draw maps, get to know the natives (if there are any), and make them fear the 'others', or simply put, your rivals.

You won't keep this secret forever. But this should give you a headstart.

PS: I know, executing the sailers is not a nice move, but hey! We are talking about a feudal society, so what measure is a commoner?

Get the Church involved

The One True Faith, as followed by all pious kingdoms, is fond of meddling in the affairs of kings whenever it brings them power and profit, and prone to making divine decrees about who can do what, where, and on what holy days.

It is also most becoming of a godly king to share news of this discovery with the Highest of Priests because clearly God(s) intended you to discover this continent, extract its wealth and share it with his/her/their church. Now that you think about it, the idea to explore west came to you in a vision, didn't it? It must be God's plan that this new land be yours, and yours alone - and with promises of enough gold, the priesthood will decree such to your neighbouring kings, giving you leeway to explore and exploit.

As other answers have noted, it's extraordinarily and impractically difficult to keep the New World a secret, especially if there's anything particularly valuable there. You'll be sending well-equipped ships out to the middle of nowhere and you're also suddenly selling a lot of exotic goods. Someone's going to put two and two together really fast. But equal knowledge does not mean equal outcome.

When your ship came back you were extremely confused. Surely the messengers made a mistake. The ship had been gone for half a year and set out with a month's worth of food. All hope for the return of the ship was gone and they were declared lost at sea months ago. But surely enough you meet with the captain who should be long dead and he tells you of an amazing new continent that he only discovered because as he was running low on supplies when he miraculously found a large island where he was able to stock up on provisions. You immediately start on a plan to colonise that island.

The trip is too long to make without a stop and you now have control of the only known place to resupply.

Even if your rivals know where the new continent is and how to get there, it does them no good if they starve before they get there. You now have a pretty strong monopoly on travel to the New World until new places to resupply are found, travel times decrease due to better technology/knowledge of trade winds, or the amount of time at sea can be increased.

As to why there's a cap on your travel time, I would suggest scurvy whose exact mechanism was not well understood until the early 1900s. (because experimentation or processing often broke down the critical vitamin C leading to bizarrely conflicting results) If high vitamin C foods are not widely available in that part of the world, it could be a long time before anyone figures it out.

So long as you aren't extracting huge amounts of wealth from the New World and allow other countries to resupply a few of their ships at your midway point every once in a while (provided they pay you a generous fee, of course), you're likely to enjoy the vast majority of the profits and not piss off your neighbours. Though those colonists might start getting uppity when they realise how important they are...

1. Barrier islands. The main currents and prevailing winds direct ships through a dangerous archipelago with many reefs.




2. Secret concession. The captain strikes a deal with the natives. He will teach them advanced shipbuilding techniques and better armaments so they can defend themselves against invasion by nations from his civilization in exchange for a trade concession for him and his crew. Then he refuses to divulge the source of his newfound wealth upon his return. If compelled, he gives a route that passes the wrong way through the archipelago.




3. Swarmbunkles. Like barnicles, but they can swim by expelling squirts of water. They swarm ships and attach to the hulls, suddenly and dramatically increasing drag and weight.




4. Sea monsters. Especially monsters that feed mostly on swarmbunkles.




5. Poison gas. Active volcanoes that spew gasses that are filtered through strange micro-organisms (thermophiles) that grow inside the volcano and secrete a hallucinogenic mist.

I'll go from actual history here and say, if there's no printing press yet, potentially indefinitely. If there's widespread use of printing presses, everyone will probably find out within a year. The two kinds of information dissemination are that different.

The North American continent was actually discovered by Leif Erikson in the year 999. There was a settlement in nearby Greenland that knew about it for the next 400 years. This settlement was officially attached to Iceland, which was in turn ruled by either Norway or Denmark, for most of that period. The Vatican also knew about the Greenland settlements, as they periodically had to send priests to it (or at least tried to).

So the information about its existence was there, nobody was particularly trying to hide it even. However maps made in mainland Europe as late at 1474 didn't show it (while showing several other rumored Atlantic islands that didn't exist). The "secret" was effectively unknown in Europe.

So the colony dies sometime after 1408, the Printing Press is invented in 1437(ish), in use all over Europe by 1480.

Now a European finds the islands near this continental landmass again in 1492. Upon his return, his letter about it leaks to the presses within a month, and the news is all over Europe.

So its pretty clear what the difference is. If you've got only medieval communications tech (no printing presses), you can easily keep it a secret for centuries. If your society has mass printing, you'll be doing better than the Spaniards if you get 2 months.

Your crew is a small number of patriots who believe in the cause

It might be worth setting it up so the crew of the ship have basically agreed to keep their discovery mission (prior to departure) secret, and having loyalty to their homeland, agree to do so. Killing the entire crew would just raise questions, and if they've already made landfall after discovery they likely already told somebody.

However, if the crew are patriotic and know it's important for the good of their nation and people to keep quiet (and maybe some riches from the new world to help buy their silence), you can keep it under wraps.

But this assumes no other country has spied the activities, or haven't also thought about a voyage in the same direction, and that no patriot in the group is feeling rather treasonous (might make for good suspense and 'what if' red herrings).

So it might make additional sense if it's a particularly dangerous journey and only the most capable sailors with the best ships are able to achieve such feats of seafaring to reach the destination (think Bermuda triangle style).

The real question you'll need to ask is how can you effectively exploit the land without tipping off anybody that it's there (IE people might notice if you have a fleet of trade ships going off and then returning back with piles of gold).

Send some colonists there with a pretense of being curious explorers. Make a big deal about the ships that never came back. For the ones that do come back, send them out with no fanfare and go the wrong direction until out of sight of land.

In the real world, John Cabot explored the east coast of North America within five years of Columbus' return from the Bahamas.

Similarly, John Sutter was utterly unable to keep the discovery of gold at Sutter's Mill secret. California was inundated with "Forty-Niners" within two years.

Your best hope is in the best policies of the Spanish, the English, and the Dutch:

• The Spanish established a 20 percent income tax on the profits of the conquistadores' ventures.



• The Spanish also sent missionaries with the conquistadores. Even if the conquistadores were not especially loyal, the missionaries set up local churches, schools, and other "hearts and minds" efforts that did bind the Spanish colonies to Spain.




• The English and Dutch invested in seamanship technologies. Some of these technologies (such as spyglasses) could be kept secret. Others, such as training methods for sailors and officers, were hard to replicate. Other technologies included watches, accurate star charts, and limes.




• The English established a network of botanical gardens, so that plants discovered in one location could be used to seed plantations in other parts of the world.




• The English also established marketplaces subject to English common law. Entire regions would re-orient their economies to focus on the trading opportunities that these marketplaces made possible.

Send the crew back there

Instead of arresting/killing the crew, as others have suggested, send them back to the continent. Send only a few ships with the purpose of populating and then fortifying a colony. That way, most of the people who know about the continent are there and can't tell anyone. If you find anyone who starts to see what's going on, have them disappear to the continent, too.

Use a fake disease

When your neighboring countries find out your ships have been traveling to the west, tell them that only one of the ships that left to a small jungle island came back, with only a tenth of the crew. Say that a mysterious illness killed everyone else. Tell them that you sent the ship back to quarantine the disease. You can say that all later outgoing ships were people who had been found to have the disease so you could stop the spread. Even when they plainly observe your ships leaving to the west, they will think it's to get rid of an infection and they will think it is a small island, not an entire continent.

Let no one return

When people find out you've been lying about the disease, they still might not know it is a continent, not an island. Refuse to give the coordinates, or give fake ones. Tell your colonies via another voyage to kill anyone from another country. That way, your claims will be supported by the absence of anyone coming back from any nation.

Let the colony grow

Eventually, the nations will find out what has been happening and they will send their naval fleets out to take the continent by force. Hopefully, when they get there, they will find the entire continent fortified and populated by people from your country. Now, the continent is officially yours and you can do whatever you want with it.