Horse having one drink after another (6)
I believe the answer is:
chaser
I believe this clue is a double definition.
'horse' is the first definition.
(I've seen this before)
'one drink after another' is the second definition.
(I've seen this before)
'having' is the link.
(Other definitions for chaser that I've seen before include "Pursuit cannon; one engraving" , "Different kind of drink - horse" , "Beer after whisky, say (or vice versa)" , "A drink like beer after whisky" , "Milder drink taken after a stronger one" .)