Conservative whip in conflict (5)
I believe the answer is:
clash
'conflict' is the definition.
(I know that clash is a more specific form of the action conflict)
'conservative whip' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'whip' becomes 'lash' (synonyms).
'c'+'lash'='CLASH'
'in' acts as a link.
(Other definitions for clash that I've seen before include "Forceful disagreement" , "Fail to fit" , "Conflict; be incompatible" , "Conflict, discord" , "Punk group; disagree" .)