Bess's partner heading off for wild party (4)
I believe the answer is:
orgy
'wild party' is the definition.
(I've seen this before)
'bess's partner heading off' is the wordplay.
'bess's partner' becomes 'porgy' (ref to opera Porgy and Bess).
'heading off' means to remove the first letter.
'porgy' with its initial letter removed is 'ORGY'.
'for' acts as a link.
(Other definitions for orgy that I've seen before include "Riotous celebration" , "Licentious revel" , "Wild revel" , "Frenzy; bacchanalia" , "Very intimate get-together" .)