Look endlessly for celebrity (4)
I believe the answer is:
star
'celebrity' is the definition.
(I've seen this before)
'look endlessly' is the wordplay.
'look' becomes 'stare' (stare is a kind of look).
'endlessly' means to remove the last letter.
'stare' with its last letter taken away is 'STAR'.
'for' is the link.
(Other definitions for star that I've seen before include "Twinkling celestial body" , "Celestial point of light" , "Famous actor" , "Lead actor" , "Top performer" .)