Chatter involving defrocked Lima bishop? (7)

I believe the answer is:

primate

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'bishop?' is the definition.
(I've seen this before)

'chatter involving defrocked lima' is the wordplay.
'chatter' becomes 'prate' (synonyms).
'involving' is an insertion indicator.
'defrocked lima' becomes 'im' (I can't explain this - if you can you should give a lot more credence to this answer).
'prate' going around 'im' is 'PRIMATE'.

Can you help me to learn more?

(Other definitions for primate that I've seen before include "Capuchin could be such" , "Chief priest" , "bishop, perhaps" , "Leader" , "Man (or monkey)" .)

I've seen this clue in The Times.

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