A bit of tranquillity on the radio (5)
I believe the answer is:
piece
'a bit of' is the definition.
(I've seen this before)
'tranquillity on the radio' is the wordplay.
'tranquillity' becomes 'peace' (peace is a kind of tranquillity).
'on the radio' indicates a 'sounds like' (homophone) clue.
'peace' is a homophone of 'PIECE'.
(Other definitions for piece that I've seen before include "One part of a whole" , "Portion; musical work" , "Firearm -- collector's item" , "A bit of something" , "Bit; item" .)