Bring out priest about it (6)
I believe the answer is:
elicit
'bring out' is the definition.
(thesaurus)
'priest about it' is the wordplay.
'priest' becomes 'eli' (I've seen this before).
'about' becomes 'c' (abbreviation for 'circa'**).
'eli'+'c'+'it'='ELICIT'
(Other definitions for elicit that I've seen before include "Draw out or bring forth" , "Evoke (a response)" , "Draw out, call forth" , "Draw out from, say meaning" , "Worm out" .)