Ape an archbishop? (7)

I believe the answer is:

primate

I believe this is a double definition.

'ape' is the first definition.
(thesaurus)

'an archbishop?' is the second definition.
(thesaurus)

(Other definitions for primate that I've seen before include "Leader" , "senior clergyman" , "Capuchin could be such" , "Metropolitan" , "Archbishop of York, for example" .)

I've seen this clue in The Times.

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