Advertising bird hunt (5)
I believe the answer is:
prowl
'hunt' is the definition.
(I've seen this before)
'advertising bird' is the wordplay.
'advertising' becomes 'PR' (public relations).
'bird' becomes 'owl' (owl is a kind of bird).
'pr'+'owl'='PROWL'
(Other definitions for prowl that I've seen before include "Move stealthily (as tiger)" , "Move stealthily around" , "Restlessly roam around" , "Skulk" , "Nose around" .)