Pursue audibly quiet part of violin (9)
I believe the answer is:
tailpiece
'part of violin' is the definition.
(I know that violin has part or parts tailpiece)
'pursue audibly quiet' is the wordplay.
'pursue' becomes 'tail' (tailing is a kind of pursuing).
'audibly' shows a homophone (sound like).
'quiet' becomes 'peace' (I've seen this before).
'peace' sounds like 'piece'.
'tail'+'piece'='TAILPIECE'
(Other definitions for tailpiece that I've seen before include "violin section" , "end" , "Last part" , "violin part" , "Final part" .)