Ring church about that man (5)
I believe the answer is:
chime
'ring' is the definition.
(eg a bell chimes or rings)
'church about that man' is the wordplay.
'church' becomes 'ce' (Church of England).
'about' indicates putting letters inside.
'that man' becomes 'him' (him refers to a man).
'ce' enclosing 'him' is 'CHIME'.
(Other definitions for chime that I've seen before include "(Of bells) ring" , "Bell's sound" , "Clang" , "(Bell) sound the hour" , "Ring; harmonise" .)