Drink after drink for horse (6)
I believe the answer is:
chaser
I believe this is a double definition.
'drink after drink' is the first definition.
(I've seen this before)
'for horse' is the second definition.
(type of horse)
(Other definitions for chaser that I've seen before include "Drink taken after another" , "Milder drink taken after a stronger one" , "Beer after whisky - follow that!" , "Drink that follows immediately after another one" , "Horse; drink following another" .)