Conservative baboon in cloak (4)
I believe the answer is:
cape
'cloak' is the definition.
(I know that cape is a type of cloak)
'conservative baboon' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'baboon' becomes 'ape' (I've seen this in another clue).
'c'+'ape'='CAPE'
'in' is the link.
(Other definitions for cape that I've seen before include "Cloak, robe" , "Batman has one" , "Headland - garment" , "Covering for the shoulders" , "Wrath perhaps" .)