... limps badly approaching school dunce (9)
I believe the answer is:
simpleton
'dunce' is the definition.
(I've seen this before)
'limps badly approaching school' is the wordplay.
'badly' indicates an anagram.
'approaching' means one lot of letters go next to another.
'school' becomes 'eton' (famous UK public school).
'limps' anagrammed gives 'simpl'.
'simpl'+'eton'='SIMPLETON'
(Other definitions for simpleton that I've seen before include "Dunce" , "Ninny" , "One very slow" , "Ass" , "Dope" .)