Quiet dash to sty (3)
I believe the answer is:
pen
'sty' is the definition.
(both can mean an animal enclosure)
'quiet dash' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'dash' becomes 'en' (I can't explain this - if you can you should believe this answer much more).
'p'+'en'='PEN'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for pen that I've seen before include "International Association of poets, playwrights etc" , "Enclosure; a swan" , "Prison" , "record" , "Swan for the writer" .)