Prisoner's right to support existence (5)
I believe the answer is:
lifer
'prisoner's' is the definition.
(lifer is a kind of prisoner)
'right to support existence' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to support' says to put letters next to each other (in a down clue, some letters hold others up).
'existence' becomes 'life' (life is a kind of existence).
'r' after 'life' is 'LIFER'.
(Other definitions for lifer that I've seen before include "person given sizeable bird" , "Long-term prisoner" , "convict given longest sentence" , "Serious criminal" , "Con" .)