Conservative arguing and boasting (7)
I believe the answer is:
crowing
'boasting' is the definition.
(crowing is a kind of boasting)
'conservative arguing' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'arguing' becomes 'rowing' (I've seen this before).
'c'+'rowing'='CROWING'
'and' is the link.
(Other definitions for crowing that I've seen before include "Being boastful" , "Boasting" .)