Drink with graduate after dance (5)
I believe the answer is:
rumba
'dance' is the definition.
(rumba is a type of dance)
'drink with graduate' is the wordplay.
'drink' becomes 'rum' (rum is a kind of drink).
'with' says to put letters next to each other.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'rum'+'ba'='RUMBA'
'after' acts as a link.
(Other definitions for rumba that I've seen before include "one's on the floor for it" , "Cuban folk-dance" , "One from Cuba" , "Latin beat" , "Burma (anag)" .)