Curate's beginning to manage church — a critical moment (6)
I believe the answer is:
crunch
'a critical moment' is the definition.
(thesaurus)
'curate's beginning to manage church' is the wordplay.
'beginning to' suggests taking the first letters.
'manage' becomes 'run' (both can mean to organise).
'church' becomes 'ch' (common abbreviation).
The first letter of 'curate' is 'c'.
'c'+'run'+'ch'='CRUNCH'
(Other definitions for crunch that I've seen before include "Decisive moment" , "Informally, a decisive event or showdown" , "Bite noisily - moment of decision" , "Chew something hard" , "Process (lots of data)" .)