Put nothing in and look petulant (4)
I believe the answer is:
pout
'look petulant' is the definition.
(I've seen this before)
'put nothing in' is the wordplay.
'nothing' becomes 'O' (looks like zero - 0).
'in' means one lot of letters goes inside another.
'put' placed around 'o' is 'POUT'.
'and' is the link.
(Other definitions for pout that I've seen before include "Petulant look; fish" , "shows disappointed face" , "set of lips" , "Push lips out in petulance" , "Purse lips sulkily" .)