Agree that man should come into church (5)
I believe the answer is:
chime
'agree' is the definition.
(thesaurus)
'man should come into church' is the wordplay.
'man' becomes 'him' ().
'should come into' indicates putting letters inside.
'church' becomes 'CE' (abbreviation for Church of England).
'him' going into 'ce' is 'CHIME'.
'that' acts as a link.
(Other definitions for chime that I've seen before include "Harmonise, peal" , "(Bell) sound the hour" , "(Of bells) ring" , "Bell's sound" , "Tuned bell" .)