Primate embraces son in part of church (4)
I believe the answer is:
apse
'part of church' is the definition.
('apse' is part of 'church')
'primate embraces son' is the wordplay.
'primate' becomes 'ape' (I've seen this before).
'embraces' indicates putting letters inside.
'son' becomes 's'.
'ape' placed around 's' is 'APSE'.
'in' is the link.
(Other definitions for apse that I've seen before include "In sacred space" , "Strange peas in the church recess" , "Where you could find a magistrate's chair" , "Church recess with domed or arched roof" , "where praetor sat" .)