Cheeky caress embracing redhead (4)
I believe the answer is:
pert
'cheeky' is the definition.
(thesaurus)
'caress embracing redhead' is the wordplay.
'caress' becomes 'pet' (petting is a kind of caressing**).
'embracing' is an insertion indicator.
'redhead' becomes 'r' (the head/first letter of 'red').
'pet' placed around 'r' is 'PERT'.
(Other definitions for pert that I've seen before include "Saucy, lively" , "Irreverent or saucy" , "Saucy and chipper" , "Impudent, cheeky" , "Persian expert" .)