Taught one conceited fellow - the Italian (5)
I believe the answer is:
pupil
'taught one' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'conceited fellow the italian' is the wordplay.
'conceited fellow' becomes 'pup' (I am not sure about this - if you are sure you should believe this answer much more).
'the italian' becomes 'il' ('the' in Italian).
'pup'+'il'='PUPIL'
Can you help me to learn more?
(Other definitions for pupil that I've seen before include "Scholar" , "Dark centre of the eye" , "Eye's centre" , "bit of a looker" , "that shrinks from brightness" .)