One going after drink (6)
I believe the answer is:
chaser
'one going after drink' is the definition.
'chaser' can be an answer for 'drink' (I've seen this before). I'm unsure of the 'one going after' bit.
'going after drink' is the wordplay.
'going' becomes 'ser' (I am not sure about this - if you are sure you should believe this answer much more).
'after' says to put letters next to each other.
'drink' becomes 'cha' (cha can mean tea).
'ser' after 'cha' is 'CHASER'.
Can you help me to learn more?
(Other definitions for chaser that I've seen before include "engraver" , "Huntsman" , "A drink like beer after whisky" , "Follow-up drink" , "Hunter; drink" .)