Cooked pig liver, edible starter? That's right (9)
I believe the answer is:
privilege
'right' is the definition.
(privilege is a kind of right)
'cooked pig liver edible starter?' is the wordplay.
'cooked' indicates anagramming the letters.
'starter?' indicates taking the first letters (I've seen 'starters' mean this).
The first letter of 'edible' is 'e'.
'pig'+'liver'='pigliver'
'pigliver' anagrammed gives 'privileg'.
'privileg'+'e'='PRIVILEGE'
'that's' is the link.
(Other definitions for privilege that I've seen before include "Advantage of one group denied to others" , "Class advantage" , "Special advantage" , "advantage given only to a few" , "Exclusive right" .)