Bess's partner heading off for wild celebration (4)
I believe the answer is:
orgy
'wild celebration' is the definition.
'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 taken off is 'ORGY'.
'for' acts as a link.
(Other definitions for orgy that I've seen before include "Excessive indulgence" , "Bacchanal" , "Overindulgent revel" , "Unrestrained revel" , "overindulgence" .)