A little bit of quiet on the radio (5)
I believe the answer is:
piece
'a little bit' is the definition.
'quiet on the radio' is the wordplay.
'quiet' becomes 'peace' (I've seen this before).
'on the radio' shows a homophone (sound like).
'peace' is a homophone of 'PIECE'.
'of' is the link.
(Other definitions for piece that I've seen before include "Musical composition" , "Section; firearm" , "Bit - part" , "Chessman - part - firearm" , "American gun" .)