Greed for caviare, perhaps (7)
I believe the answer is:
avarice
'greed' is the definition.
(avarice is a kind of greed)
'caviare perhaps' is the wordplay.
'perhaps' indicates anagramming the letters.
'caviare' is an anagram of 'AVARICE'.
'for' is the link.
(Other definitions for avarice that I've seen before include "Eager desire" , "Cupidity" , "A deadly sin" , "One of seven deadly sins" , "Greed - caviare (anag)" .)