Drunk greeting we hear (4)
I believe the answer is:
high
'drunk' is the definition.
(I've seen this before)
'greeting we hear' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'we hear' indicates a 'sounds like' (homophone) clue.
'hi' sounds like 'HIGH'.
(Other definitions for high that I've seen before include "American school" , "Way up" , "Far above ground level" , "having senior ranking?" , "First-rate - drunk" .)