Cook disturbed by a noisy quarrel (4)
I believe the answer is:
fray
'noisy quarrel' is the definition.
'cook disturbed by a' is the wordplay.
'cook' becomes 'fry' (fry cook is a kind of cook).
'disturbed by' is an insertion indicator.
'fry' placed around 'a' is 'FRAY'.
(Other definitions for fray that I've seen before include "Wear away at the edges" , "Battle - loose at the edges!" , "Combat - wear" , "Become worn at the edges" , "Become ragged" .)