A nit, one silly schoolboy (7)
I believe the answer is:
etonian
'schoolboy' is the definition.
(I've seen this before)
'a nit one silly' is the wordplay.
'silly' indicates anagramming the letters.
'a'+'nit'+'one'='anitone'
'anitone' anagrammed gives 'ETONIAN'.
(Other definitions for etonian that I've seen before include "Relating to one particular school" , "English student" , "Public school boy" , "Public schoolboy" , "student in establishment?" .)