Cold primate wants shawl (4)
I believe the answer is:
cape
'shawl' is the definition.
(I've seen this before)
'cold primate' is the wordplay.
'cold' becomes 'c' (eg on taps).
'primate' becomes 'ape' (large primate).
'c'+'ape'='CAPE'
'wants' is the link.
(Other definitions for cape that I've seen before include "Wrath, say" , "Shoulders? They're covered in it" , "Cod, for example" , "Shawl" , "Outer garment" .)