Briefly, drink up, carrying a little one for me too (4,3,4)
I believe the answer is:
join the club
'briefly drink up' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.
'a little one for me too' is the wordplay.
I cannot really understand how this works, but
'little' could be 'l' (abbreviation for little) and 'l' is found in the answer.
'one' could be 'the' (both can introduce a definite example of something) and 'the' is found in the answer.
'me' could be 'i' and 'i' is found within the answer.
This explanation may well be incorrect...
'carrying' is the link.
Can you help me to learn more?
(Other definitions for join the club that I've seen before include "Girl's pregnant" , "We're both in that difficult situation!" , "I have just the same problem!" , "What you do if you sign for United" , "Things are just as bad for me!" .)