Cold primate demands 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'
'demands' acts as a link.
(Other definitions for cape that I've seen before include "Cod possibly" , "Wrap" , "Cloak or headland (4)" , "Loose cloak or promontory" , "Wrath perhaps" .)