Mark of rank priest in trouble (6)
I believe the answer is:
stripe
'mark of rank' is the definition.
(I've seen this before)
'priest in trouble' is the wordplay.
'in trouble' is an anagram indicator.
'priest' anagrammed gives 'STRIPE'.
(Other definitions for stripe that I've seen before include "Thin band of colour" , "Braid showing military rank" , "promotion, maybe" , "Length of material, maybe showing rank" , "Sign of a soldier's rank" .)