The dunce possibly limps to school (9)
I believe the answer is:
simpleton
'the dunce' is the definition.
(I've seen this before)
'possibly limps to school' is the wordplay.
'possibly' indicates anagramming the letters.
'to school' becomes 'eton' (famous UK public school).
'limps' anagrammed gives 'simpl'.
'simpl'+'eton'='SIMPLETON'
(Other definitions for simpleton that I've seen before include "Natural" , "Simon for one" , "Dope" , "Foolish or gullible person" , "Dunce" .)