Urge principal to become an intellectual (7)
I believe the answer is:
egghead
'an intellectual' is the definition.
(I know that egghead is a type of intellectual)
'urge principal' is the wordplay.
'urge' becomes 'egg' (as in egging someone on).
'principal' becomes 'head' (synonyms).
'egg'+'head'='EGGHEAD'
'to become' is the link.
(Other definitions for egghead that I've seen before include "brain" , "Expert" , "Brainiac" , "Cracked" , "Brainbox" .)