Primate controls small section of church (4)
I believe the answer is:
apse
'section of church' is the definition.
(I've seen this in other clues)
'primate controls small' is the wordplay.
'primate' becomes 'ape' (large primate).
'controls' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'ape' going around 's' is 'APSE'.
(Other definitions for apse that I've seen before include "Primate holds saint to be a" , "Domed section of a church" , "inside church?" , "Church area" , "Where you could find a magistrate's chair" .)