Theatrical piece by doctor, an arts graduate (5)
I believe the answer is:
drama
'theatrical piece' is the definition.
(I've seen this before)
'by doctor an arts graduate' is the wordplay.
'by' is a charade indicator (letters next to each other).
'doctor' becomes 'Dr' (abbreviation).
'an' becomes 'a'.
'arts graduate' becomes 'MA' (Master of Arts).
'dr' next to 'a' is 'dra'.
'dra'+'ma'='DRAMA'
(Other definitions for drama that I've seen before include "Theatrical performance" , "Plays as branch of literature" , "Literary play" , "sensation" , "Play (as a genre)" .)