That would be a disaster for the British. Holding New York largely cut New England off from the other colonies. It was the single most significant Loyalist stronghold and the base of operations for an extremely large contingent.
Honestly, this could end the American theater of the war at a stroke. The British hadn't even begun their attempt to take the Deep South at this point. They couldn't run much of a war from Florida, Rhode Island, and Halifax. Even if they tried the effort would be immeasurably more difficult against a contiguous state and they would be quite aware of the fact.
At a guess? Britain offers a separate peace to the Americans. They hand over the Floridas and proto-Ontario, perhaps throwing in pre-Quebec or Nova Scotia for good measure. Essentially, they concede whatever it takes to ensure the Americans are formally at peace immediately. They wouldn't part with the Caribbean holdings, Bermuda, Newfoundland, or the HBC's claims, but everything else is on the table.
Assuming they can get the Americans to agree, they then turn on the alliance facing them. All told France, Spain, and especially the Dutch do less well out of the war. Possibly there is an earlier French bankruptcy, with all that entails.