Graduate after drink and a dance (5)
I believe the answer is:
rumba
'a dance' is the definition.
(rumba is a kind of dance)
'graduate after drink' is the wordplay.
'graduate' becomes 'ba'.
'after' says to put letters next to each other.
'drink' becomes 'rum' (I've seen this before).
'ba' after 'rum' is 'RUMBA'.
'and' is the link.
(Other definitions for rumba that I've seen before include "South American dance" , "number of steps" , "What to perform" , "Lively Cuban dance" , "Dance originating in Cuba" .)