Music graduate seen after drink (5)
I believe the answer is:
rumba
'music' is the definition.
(rumba is a kind of music)
'graduate seen after drink' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'seen after' is a charade indicator (letters next to each other).
'drink' becomes 'rum' (rum is a kind of drink).
'ba' put after 'rum' is 'RUMBA'.
(Other definitions for rumba that I've seen before include "Afro-Cuban or ballroom dance" , "Caribbean dance" , "Style of dance" , "Latin American dance" , "One from Cuba" .)