Beginning, not ending, as celebrity (4)
I believe the answer is:
star
'celebrity' is the definition.
(a star is a celebrity or famous person)
'beginning not ending' is the wordplay.
'beginning' becomes 'start' (synonyms).
'not ending' means to remove the last letter.
'start' with its last letter taken off is 'STAR'.
'as' acts as a link.
(Other definitions for star that I've seen before include "virtuoso" , "Chaste, pure" , "A heavenly body or film favourite" , "Heavenly light" , "Leading character" .)