Greed, a weakness gripping a Republican (7)
I believe the answer is:
avarice
'greed' is the definition.
(avarice is a kind of greed)
'a weakness gripping a republican' is the wordplay.
'weakness' becomes 'vice' (I've seen this in another clue).
'gripping' means one lot of letters goes inside another (inserted letters are gripped).
'republican' becomes 'R' (abbreviation).
'a'+'r'='ar'
'vice' placed around 'ar' is 'varice'.
'a'+'varice'='AVARICE'
(Other definitions for avarice that I've seen before include "Greed, covetousness" , "Greed - caviare (anag)" , "Sway, control" , "Insatiable lust" , "excessive desire for wealth" .)