Lightly hit cold cheek (4)
I believe the answer is:
clip
'lightly hit' is the definition.
'clip' can be an answer for 'hit' (thesaurus). I am not certain of the 'lightly' bit.
'cold cheek' is the wordplay.
'cold' becomes 'c' (eg on taps).
'cheek' becomes 'lip' (both can mean insolence or rudeness).
'c'+'lip'='CLIP'
Can you help me to learn more?
(Other definitions for clip that I've seen before include "Shorten" , "Device for holding papers together" , "Fastener - part of film" , "Short piece of film" , "Prune" .)