Bit of quiet, say (5)
I believe the answer is:
piece
'bit of' is the definition.
(I've seen this before)
'quiet say' is the wordplay.
'quiet' becomes 'peace' (I've seen this before).
'say' indicates a 'sounds like' (homophone) clue.
'peace' is a homophone of 'PIECE'.
(Other definitions for piece that I've seen before include "A part of something" , "Single article" , "newspaper article" , "Bit - part" , "Musical work; bit" .)