Conservative leading referendum vote that’s split (6)
I believe the answer is:
cleave
'that's split' is the definition.
(synonyms)
'conservative leading referendum vote' is the wordplay.
'leading' indicates taking the first letters.
'referendum vote' becomes 'leave' (as opposed to remain in the UK EU referendum).
The first letter of 'conservative' is 'c'.
'c'+'leave'='CLEAVE'
(Other definitions for cleave that I've seen before include "Unite together; split apart" , "Split or cling to" , "Crack" , "Chop or split" , "Join or split" .)