Satisfy with a contract on the quiet (6)
I believe the answer is:
please
'satisfy' is the definition.
(I know that please is a more specific form of the action satisfy)
'contract on the quiet' is the wordplay.
'contract' becomes 'lease' (leasing is a kind of contracting).
'on' says to put letters next to each other.
'the quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'lease' put after 'p' is 'PLEASE'.
'with a' is the link.
(Other definitions for please that I've seen before include "Give satisfaction to" , "See pal (anag) -- charm" , "Delight, gladden" , "Cause to feel happy" , "Cause (someone) to feel satisfied" .)