Who's in charge of bishops? Big ape, perhaps (7)

I believe the answer is:

primate

I believe this is a double definition.

'who's in charge of bishops?' is the first definition.

'big ape perhaps' is the second definition.

(Other definitions for primate that I've seen before include "Highest-ranking bishop" , "Man (or monkey)" , "Man in the mitre" , "Higher mammal" , "Archbishop - monkey, perhaps" .)

I've seen this clue in The Everyman puzzle in The Observer.

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