Dismiss through drink (4)
I believe the answer is:
sack
I believe this clue is a double definition.
'dismiss' is the first definition.
(I know that dismiss can be written as sack)
'drink' is the second definition.
(sack is a kind of drink)
'through' is the link.
(Other definitions for sack that I've seen before include "Big, coarse bag" , "Fire; hessian bag" , "present holder" , "Large hessian bag" , "Destruction" .)