Expressionist composer's chosen new pupil of his (10)
I believe the answer is:
schoenberg
'expressionist composer's' is the definition.
'schoenberg' can be an answer for 'composer's' (I've seen this before). I'm not sure about the 'expressionist' bit.
'chosen new pupil of his' is the wordplay.
'new' is an anagram indicator.
'pupil of his' becomes 'berg' (I can't explain this - if you can you should believe this answer much more).
'chosen' with letters rearranged gives 'schoen'.
'schoen'+'berg'='SCHOENBERG'
Can you help me to learn more?
(Other definitions for schoenberg that I've seen before include "Austrian scorer" , "Arnold --, Austrian-born composer" .)