This 20 year period saw the 13 colonies become a nation and wage war against the best army in the world, that of mother-country Great Britain. Immigration from Europe slowed to a halt. There were a few European military officers who came over to help the cause of Independence. Much of the movement was west into the Kentucky and Ohio country.
1763 - 1783: Scots, Scots-Irish, Northern English, Dutch, Germans and Swedes continue to enter the colonies.* Many move into the western frontier. Slave trade and indentured servitude continues.
1775: Daniel Boone leads settlers into Kentucky.
1776 - 1783: Unwelcome arrival of British and Hessian soldiers in the US.
By the end of the American Revolution, a large number of Hessian soldiers who had been captured or deserted elected to stay in the States.
*I had very few ancestors arrive in the Colonies/States during this period. Dr. Peter Trisler may have been the only one. Probably 85 - 90% of my ancestors were residing in the US by war's end.