You can unlock the Barbarian King at Town Hall 7, and after that, he can reach a certain maximum level at every Town Hall. You cannot upgrade your Barbarian King beyond these max level caps. Here are the max levels of Barbarian King:

You can unlock the Archer Queen at Town Hall 9, and after that, she can reach a certain maximum level at every Town Hall. You cannot upgrade your Archer Queen beyond these max level caps. Here are the max levels of Archer Queen: