Primate carrying son in church recess (4)
I believe the answer is:
apse
'church recess' is the definition.
(part of a church)
'primate carrying son' is the wordplay.
'primate' becomes 'ape' (large primate).
'carrying' is an insertion indicator.
'son' becomes 's' (genealogical abbreviation for son).
'ape' enclosing 's' is 'APSE'.
'in' is the link.
(Other definitions for apse that I've seen before include "Peas (anag) - found in church" , "Church's part" , "Rounded end of building" , "space for altar" , "may be seen in church!" .)