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.
(type of horse)
'one drink after another' is the second definition.
(I've seen this before)
'having' acts as a 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" .)