Primate going to prison gets a snack (6)
I believe the answer is:
canape
'a snack' is the definition.
(I've seen this before)
'primate going to prison' is the wordplay.
'primate' becomes 'ape' (I've seen this before).
'going to' is a charade indicator (letters next to each other).
'prison' becomes 'can' (the can is American slang for prison).
'ape' after 'can' is 'CANAPE'.
'gets' is the link.
(Other definitions for canape that I've seen before include "Savoury appetiser, often accompanied by Champagne" , "Tasty morsel, with drinks perhaps" , "Savoury party fare" , "Small savoury on toast or bread" , "Hors d'oeuvre" .)