Manage priest’s cloak (4)
I believe the answer is:
cope
This clue might be a double definition.
'manage priest's' is the first definition.
'cope' can be an answer for 'manage' (manage can mean to cope or do well). I am not certain of the 'priest's' bit.
'cloak' is the second definition.
(cloak worn by a bishop)
Can you help me to learn more?
(Other definitions for cope that I've seen before include "Firmly based (in)" , "Manage, subsist" , "Join" , "Deal effectively (with something difficult)" , "Rise to the occasion" .)