Quiet desire to have a fling? (5)
I believe the answer is:
pitch
'a fling?' is the definition.
(I know that pitch is a kind of fling)
'quiet desire' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'desire' becomes 'itch' (itch is a kind of desire).
'p'+'itch'='PITCH'
'to have' acts as a link.
(Other definitions for pitch that I've seen before include "Street seller's location" , "Sales talk - where games are played" , "settle" , "Area for games" , "Residue of distillation" .)