Gawp endlessly, finding celebrity (4)
I believe the answer is:
star
'celebrity' is the definition.
(a star is a celebrity or famous person)
'gawp endlessly' is the wordplay.
'gawp' becomes 'stare' (I've seen this before).
'endlessly' means to remove the last letter.
'stare' with its last letter taken off is 'STAR'.
'finding' acts as a link.
(Other definitions for star that I've seen before include "Eg, Betelgeuse" , "Five-pointed celestial body" , "Famous player" , "Celestial body of hot gases" , "Rush" .)