Turn away, eager to miss new sullen look (4,3)
I believe the answer is:
keep out
'turn away' is the definition.
'eager to miss new sullen look' is the wordplay.
'eager' becomes 'keen' (I've seen this before).
'to miss' suggests deleting specific letters.
'new' becomes 'n'.
'sullen look' becomes 'pout'.
'keen' with 'n' removed is 'kee'.
'kee'+'pout'='KEEP OUT'
(Other definitions for keep out that I've seen before include "notice to trespassers?" , "Stay clear" , "Private land sign" , "No entry!" , "bar" .)