Band is quiet when inside (4)
I believe the answer is:
sash
'band' is the definition.
(sash is a kind of band)
'quiet when inside' is the wordplay.
'quiet' becomes 'sh'.
'when' becomes 'as'.
'inside' indicates putting letters inside.
'sh' enclosing 'as' is 'SASH'.
'is' is the link.
(Other definitions for sash that I've seen before include "Popular band in Northern Ireland" , "Framework holding window panes" , "Item of clothing - frame for glass" , "Band - scarf" , "Window frame; silk band" .)