Look for new shack outside (4)
I believe the answer is:
hunt
'look for' is the definition.
(to hunt for something is to look for it)
'new shack outside' is the wordplay.
'new' becomes 'n' (abbreviation as in New Testament NT).
'shack' becomes 'hut' (synonyms).
'outside' means one lot of letters goes inside another (some letters go outside others).
'n' put into 'hut' is 'HUNT'.
(Other definitions for hunt that I've seen before include "ARTIST" , "Racing driver" , "Look high and low" , "Meet - famous mountaineer" , "Quest" .)