Quiet follows when backing band .... (4)
I believe the answer is:
sash
'band' is the definition.
(sash is a kind of band)
'quiet follows when backing' is the wordplay.
'quiet' becomes 'sh'.
'follows' says to put letters next to each other.
'when' becomes 'as'.
'backing' says the letters should be written backwards.
'as' in reverse letter order is 'sa'.
'sh' after 'sa' is 'SASH'.
(Other definitions for sash that I've seen before include "Popular band in Northern Ireland" , "Decorative belt" , "Waistband - type of window" , "Decoration for the twelfth" , "Band worn over shoulder or round waist" .)