Party for letting go of some left-leaning minority groups (4)
I believe the answer is:
orgy
'party for letting go' is the definition.
'some left-leaning minority groups' is the wordplay.
'left' is a reversal indicator.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'ygro' is hidden within 'leaning minority groups'.
'ygro' in reverse letter order is 'ORGY'.
'of' is the link.
(Other definitions for orgy that I've seen before include "Drunken revelry" , "Drunken revel" , "Wild overindulgent party" , "wild spree" , "Wild licentious party" .)