Abbot’s deputy with previous conviction (5)
I believe the answer is:
prior
This clue is a double definition.
'abbot's deputy' is the first definition.
(I've seen this before)
'previous conviction' is the second definition.
(prior can mean a previous conviction)
'with' is the link.
(Other definitions for prior that I've seen before include "deputy head in monastery" , "Senior monk; earlier" , "head of a religious community" , "Existing beforehand" , "More important" .)