He's after you to get a second drink (6)
I believe the answer is:
chaser
'a second drink' is the definition.
(I've seen this before)
'he's after you' is the wordplay.
I cannot really see how this works, but
'he' could be 'chase' and 'chase' is found within the answer.
A single letter 'r' remains which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'to get' acts as a link.
Can you help me to learn more?
(Other definitions for chaser that I've seen before include "Racehorse - search (anag)" , "Drink taken after another" , "Hunter; drink" , "Drink of beer after spirit" , "Yellow-Dog Dingo?" .)