Right to go after being a prisoner (5)
I believe the answer is:
lifer
'a prisoner' is the definition.
(lifer is a kind of prisoner)
'right to go after being' is the wordplay.
'right' becomes 'R' (common abbreviation).
'to go after' means one lot of letters go next to another.
'being' becomes 'life' (life is a kind of being).
'r' after 'life' is 'LIFER'.
(Other definitions for lifer that I've seen before include "Rifle (anag.)" , "One with maximum sentence" , "Con" , "Convicted murderer, say" , "Long-term prisoner" .)