Celebrity needs time to get going (5)
I believe the answer is:
start
'get going' is the definition.
('start' can be a synonym of 'get going')
'celebrity needs time' is the wordplay.
'celebrity' becomes 'star' (I've seen this before**).
'needs' says to put letters next to each other.
'time' becomes 't'.
'star'+'t'='START'
'to' is the link.
(Other definitions for start that I've seen before include "launch" , "Beginning" , "Jerk" , "Onset" , "Move quickly < when surprised" .)