Bess's partner quietly leaving wild party (4)
I believe the answer is:
orgy
'wild party' is the definition.
(orgy can mean a boisterous party)
'bess's partner quietly leaving' is the wordplay.
'bess's partner' becomes 'porgy' (ref to opera Porgy and Bess).
'quietly' becomes 'p' (p for piano and quiet).
'leaving' indicates named letters should be taken away.
'porgy' with 'p' taken out is 'ORGY'.
(Other definitions for orgy that I've seen before include "Wild licentious party" , "Debauched party" , "Bacchanalian party" , "wild spree" , "Excess" .)