Go down with immoral act at Kings Head (4)
I believe the answer is:
sink
'go down' is the definition.
('sink' can be a synonym of 'go down')
'immoral act at kings head' is the wordplay.
'immoral act' becomes 'sin' (I've seen this before**).
'at' is a charade indicator (letters next to each other).
'head' suggests taking the first letters.
The first letter of 'kings' is 'k'.
'sin'+'k'='SINK'
'with' is the link.
(Other definitions for sink that I've seen before include "place of corruption" , "Drop beneath the surface" , "Drop in the ocean?" , "Droop, submerge" , "Excavate (a well)" .)