Celebrity has to begin shortly (4)
I believe the answer is:
star
'celebrity' is the definition.
(I've seen this before)
'to begin shortly' is the wordplay.
'to begin' becomes 'start' ('start' can be a synonym of 'begin').
'shortly' means to remove the last letter.
'start' with its last letter taken away is 'STAR'.
'has' acts as a link.
(Other definitions for star that I've seen before include "Asterisk" , "Famous entertainer" , "Heavenly body - leading actress?" , "Screen idol" , "Lead actor" .)