Clergyman, mostly, or museum director (7)
I believe the answer is:
curator
'museum director' is the definition.
(someone curating a museum)
'clergyman mostly or' is the wordplay.
'clergyman' becomes 'curate' (assistant to a priest).
'mostly' means to remove the last letter (most but not all of the word).
'curate' with its final letter removed is 'curat'.
'curat'+'or'='CURATOR'
(Other definitions for curator that I've seen before include "Cultural employee" , "Custodian - caretaker" , "Museum official" , "Museum custodian" , "Guardian" .)