Greed - adult weakness - possessing a Republican (7)
I believe the answer is:
avarice
'greed' is the definition.
(synonyms)
'adult weakness possessing a republican' is the wordplay.
'adult' becomes 'a' (abbreviation).
'weakness' becomes 'vice' (I've seen this before).
'possessing' is an insertion indicator.
'republican' becomes 'r' (abbreviation).
'a'+'r'='ar'
'vice' going around 'ar' is 'varice'.
'a'+'varice'='AVARICE'
(Other definitions for avarice that I've seen before include "Cupidity" , "Parsimony" , "Greed, covetousness" , "excessive desire for wealth" , "Insatiable lust" .)