Student deserved to become erudite (7)
I believe the answer is:
learned
'erudite' is the definition.
(synonyms)
'student deserved' is the wordplay.
'student' becomes 'l' (as in L-plates for learner drivers).
'deserved' becomes 'earned' (I've seen this before).
'l'+'earned'='LEARNED'
'to become' is the link.
(Other definitions for learned that I've seen before include "Having great knowledge" , "Got to know" , "Well-educated" , "Gained understanding" , "Picked up - well-read" .)