The Battle of Yorktown was the end of major engagements between the Continentals and British. Henry Clinton was replaced, North and his government were replaced, and the British and Americans for the most part wanted to see how things went in Paris.

That did not stop militia on the frontier from raiding into the Ohio Valley from Pennsylvania and Kentucky. There were some raids back and forth, but nothing that major.

In the South some Cherokee refused to honor a Treaty with the Americans and they fought on until 1785. This hatred ran deep, as the Cherokee fought the South Carolina settlers in the French and Indian War as well.

But the most major post 1781 fighting was between the Franco-Spanish Alliance (and the Dutch) and Britain. America was afraid Spain and France would try to bargain the US cause for other territories, so they cut a separate truce with Britain, but that left their old allies and Britain to slug it out. It was mostly naval actions, most notably to capture Jamaica and Gibraltar but both of those actions failed. The Battle of Saintes, 1782, was a pretty big naval engagement which saw the British defeat the Franco Spanish fleet pretty handily.

There were numerous clashes in India, Central America, and really in many places the empires were in close proximity, all after 1781. There was one battle, which apparently is the last major engagement of the war was the Bate of Cuddelore (1783), was fought in the Bay of Bengal, and was only ended when a British ship carried news of the Treaty of Paris to the combatants.

In a way, between the large powers, the American Revolution was kind of a global conflict, much of it happening in the years between 1779 and 1783 at sea between Europe's great powers.