Strange graduate's dance (5)
I believe the answer is:
rumba
'dance' is the definition.
(rumba is a type of dance)
'strange graduate's' is the wordplay.
'strange' becomes 'rum' (synonyms).
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'rum'+'ba'='RUMBA'
(Other definitions for rumba that I've seen before include "Afro-Cuban or ballroom dance" , "Cuban folk-dance" , "Style of dance" , "Lively Cuban dance" , "Caribbean dance" .)