Priest turned out to be most mature (6)
I believe the answer is:
ripest
'be most mature' is the definition.
('ripe' can be similar in meaning to 'mature')
'priest turned out' is the wordplay.
'turned out' is an anagram indicator (turn out can mean to organise).
'priest' with letters rearranged gives 'RIPEST'.
'to' is the link.
(Other definitions for ripest that I've seen before include "Most ready for harvesting or eating" , "Most mature and ready to eat" , "to be furthest from green" .)