I've made pesto, I've made pizza, I've never made pesto pizza. I've found 3 main ideas:
1: Standard pizza style: pesto on the dough, whatever other toppings, bake the whole thing.
2: Make basically a pizza bianca, baking the dough with cheese on it, then putting the pesto on & maybe other toppings, back in the oven just for a minute or two.
3: Bake the dough bare, spread pesto on baked pizza dough, maybe put other raw ingredients on.
Seems to me you want to cook the basil as little as possible. I'm leaning towards 2 or 3, but the vast majority of recipes I saw were #1s.