Should I clean the pan between batches of browning
I don't think there is a definitive answer to that.

You could remove some of the fat and small residues between batches to prevent them from burning.

You can also lower the temperature, it will take a little more time to brown the meat.

This recipe suggest to deglaze between batches and keep the juices for later use in the recipe.

http://www.thekitchn.com/recipe-template-how-to-make-be-107019