Principal following urge to be intellectual (7)
I believe the answer is:
egghead
'be intellectual' is the definition.
(thesaurus)
'principal following urge' is the wordplay.
'principal' becomes 'head' ('head' can be a synonym of 'principal').
'following' says to put letters next to each other.
'urge' becomes 'egg' (I've seen this before).
'head' after 'egg' is 'EGGHEAD'.
'to' is the link.
(Other definitions for egghead that I've seen before include "Cracked" , "Brainiac" , "Intellectual (sl.)" , "Informal intellectual of ovoid type" , "Intellectual (colloq.)" .)