Succeeded after prison cuts (5)
I believe the answer is:
nicks
'cuts' is the definition.
(I know this)
'succeeded after prison' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'after' says to put letters next to each other.
'prison' becomes 'nick' (slang term for prison).
's' put after 'nick' is 'NICKS'.
(Other definitions for nicks that I've seen before include "chips" , "Small cuts" , "Catches" , "Steals (sl.)" , "Small incisions; pinches" .)