Earlier monastery, incomplete (5)
I believe the answer is:
prior
'earlier' is the definition.
(synonyms)
'monastery incomplete' is the wordplay.
'monastery' becomes 'priory' (I've seen this before).
'incomplete' means to remove the last letter.
'priory' with its final letter taken away is 'PRIOR'.
(Other definitions for prior that I've seen before include "head of a religious community" , "Pre-existing, religious head" , "Previous; abbot's deputy" , "Existing beforehand" , "Certainly not succeeding" .)