Cut off cold insolence (4)
I believe the answer is:
clip
'cut off' is the definition.
(I've seen this in another clue)
'cold insolence' is the wordplay.
'cold' becomes 'c' (eg on taps).
'insolence' becomes 'lip' (I've seen this in another clue).
'c'+'lip'='CLIP'
(Other definitions for clip that I've seen before include "Cut short; cartridge holder" , "Cartridge holder; jewellery item" , "sort of joint" , "Fastener - part of film" , "Fastener; trim" .)