Painter supporting bishop and a German composer (9)
I believe the answer is:
bernstein
'composer' is the definition.
(Leonard Bernstein)
'painter supporting bishop and a german' is the wordplay.
'painter' becomes 'ernst' (Max Ernst).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'bishop' becomes 'B' (abbreviation for bishop in chess).
'and' says to put letters next to each other.
'a german' becomes 'ein' ('a' in German).
'ernst' put after 'b' is 'bernst'.
'bernst'+'ein'='BERNSTEIN'
(Other definitions for bernstein that I've seen before include "Mass producer" , "Noteworthy personality" , "scoring ace" , "composer" , "Leonard --, US conductor" .)