One punch after another bringing cheers (4-4)
I believe the answer is:
chin-chin
'cheers' is the definition.
(I've seen this before)
'one punch after another' is the wordplay.
'one punch' becomes 'chin' (slang term meaning to punch someone on the chin).
'after' means one lot of letters go next to another.
'another' becomes 'chin' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'chin'+'chin'='CHIN-CHIN'
'bringing' is the link.
Can you help me to learn more?
(Other definitions for chin-chin that I've seen before include "Cheers, bottoms up" , "good health ..." , "Down the hatch!" .)