Horse and Conservative hunt set out (8)
I believe the answer is:
chestnut
'horse' is the definition.
(chestnut is a kind of horse)
'conservative hunt set out' is the wordplay.
'conservative' becomes 'C' (abbreviation commonly used in UK politics).
'out' indicates an anagram (out can mean wrong or inaccurate).
'hunt'+'set'='huntset'
'huntset' with letters rearranged gives 'hestnut'.
'c'+'hestnut'='CHESTNUT'
'and' is the link.
(Other definitions for chestnut that I've seen before include "Deep reddish-brown" , "Item for stuffing" , "Wood" , "Horse coat colour" , "''Underneath the spreading . . . . . . . . tree''" .)