Noisy quarrel involving English composer in past (6)
I believe the answer is:
barney
'noisy quarrel' is the definition.
(I've seen this before)
'english composer in past' is the wordplay.
'english composer' becomes 'Arne' (Thomas Arne).
'in' means one lot of letters goes inside another.
'past' becomes 'by' (as in years gone by).
'arne' going within 'by' is 'BARNEY'.
'involving' acts as a link.
(Other definitions for barney that I've seen before include "Dust-up" , "Noisy quarrel (informal)" .)