Conservative-Labour rift (5)
I believe the answer is:
cleft
'rift' is the definition.
(thesaurus)
'conservative-labour' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'labour' becomes 'left' (I've seen this in other clues).
'c'+'left'='CLEFT'
(Other definitions for cleft that I've seen before include "Partially divided" , "Split, divided" , "Split into two" , "Split (as a stick)" , "Split; fissure" .)