I perform, learner becoming movie star? (4)
I believe the answer is:
idol
'movie star?' is the definition.
(idol can mean a celebrity)
'i perform learner' is the wordplay.
'perform' becomes 'do' (both can mean complete an action).
'learner' becomes 'l' (as in a learner driver with L-plates on their car).
'i'+'do'+'l'='IDOL'
'becoming' is the link.
(Other definitions for idol that I've seen before include "Hero of screen or stage" , "Graven image or worshipped person" , "someone admirable" , "A matinee -- is a handsome actor" , "As before, fake" .)