Intellectual urge by school principal (7)
I believe the answer is:
egghead
'intellectual' is the definition.
(egghead is a kind of intellectual)
'urge by school principal' is the wordplay.
'urge' becomes 'egg' (I've seen this before).
'by' says to put letters next to each other.
'school principal' becomes 'head' ('head' can be a synonym of 'school principal').
'egg'+'head'='EGGHEAD'
(Other definitions for egghead that I've seen before include "brain" , "Ovoid-shaped intellectual" , "Intellectual - highbrow" , "Heed gag about slang intellectual" , "may take a bashing at the breakfast table" .)