If you're just talking about park entry then no, you don't need to reserve in advance (unless heading to the parks containing chimpanzees in western Tanzania, or the gorilla and chimp parks in Uganda or Rwanda, in which case chimp/gorilla permits should be reserved months in advance).
Otherwise you can just turn up to any park and pay on the gate.
However, it’s very sensible to book accommodation in advance. It’s not usually very easy in bigger parks to drive around checking out accommodation on arrival as there can be great distances between places.
