Go downhill having imbibed a Japanese drink (4)
I believe the answer is:
saki
'japanese drink' is the definition.
(I've seen this before)
'go downhill having imbibed a' is the wordplay.
'go downhill' becomes 'ski' (I've seen this before).
'having imbibed' is an insertion indicator.
'ski' placed around 'a' is 'SAKI'.
(Other definitions for saki that I've seen before include "Short-story writer" , "Pen name of short story writer, H.H. Munro, d. 1916" , "author chosen by 29" , "Literary pseudonym of H. H. Munro" , "Pseudonymous English writer" .)