Composer taken outside about a quarrel (6)
I believe the answer is:
breach
'a quarrel' is the definition.
(thesaurus)
'composer taken outside about' is the wordplay.
'composer' becomes 'bach' (Johann Sebastian Bach).
'taken outside' means one lot of letters goes inside another.
'about' becomes 're' ('re' means regarding or about).
'bach' enclosing 're' is 'BREACH'.
(Other definitions for breach that I've seen before include "part of firearm, say" , "'A custom more 1 down in the ____ ..." , "Opening - quarrel" , "Gap made in a fortification" , "Gap in a wall or barrier" .)