After time, inquire about supporting Church’s specially-formed group (4,5)
I believe the answer is:
task force
'specially-formed group' is the definition.
'after time inquire about supporting church's' is the wordplay.
'after' is a charade indicator (letters next to each other).
'time' becomes 't'.
'inquire about' becomes 'ask' (I've seen this before).
'supporting' becomes 'for'.
'church' becomes 'ce' (abbreviation for Church of England).
't'+'ask' is 'task'.
'task'+'for'+'ce'='TASK-FORCE'
(Other definitions for task force that I've seen before include "Group organised for a specific purpose" , "working group" , "subcommittee" , "Group with a mission" , "specially-trained unit" .)