Pet shredded coat outside to some music (7)
I believe the answer is:
toccata
'some music' is the definition.
(toccata is a kind of music)
'pet shredded coat outside' is the wordplay.
'pet' becomes 'cat' (I have seen 'Common pet ' mean 'cat' so perhaps 'pet' could also mean 'cat').
'shredded' indicates anagramming the letters.
'outside' is an insertion indicator.
'coat' with letters rearranged gives 'toca'.
'cat' placed within 'toca' is 'TOCCATA'.
'to' is the link.
(Other definitions for toccata that I've seen before include "Baroque musical composition" , "Keyboard piece emphasising touch" , "Touching piece" , "technical challenge" , "High-speed keyboard piece" .)