Most mature priest, possibly (6)
I believe the answer is:
ripest
'most mature' is the definition.
('ripe' can be similar in meaning to 'mature')
'priest possibly' is the wordplay.
'possibly' indicates an anagram.
'priest' is an anagram of 'RIPEST'.
(Other definitions for ripest that I've seen before include "Most mature and ready to eat" , "to be furthest from green" , "Most ready for harvesting or eating" .)