Primate unites church with Devil (5)

I believe the answer is:

chimp

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'primate' is the definition.
(short for chimpanzee)

'church with devil' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'with' is a charade indicator (letters next to each other).
'devil' becomes 'imp' (devilish creature).
'ch'+'imp'='CHIMP'

'unites' is the link.
I am not very happy about this link. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for chimp that I've seen before include "Cheeky primate" , "Creature" , "Ape (colloq.)" , "Arboreal ape from equatorial Africa (abbr)" , "Anthropoid ape" .)

I've seen this clue in The Sun.

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