Strange graduate in music (5)
I believe the answer is:
rumba
'music' is the definition.
(rumba is a kind of music)
'strange graduate' is the wordplay.
'strange' becomes 'rum' (similar in meaning).
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'rum'+'ba'='RUMBA'
'in' is the link.
(Other definitions for rumba that I've seen before include "Ballroom dance of Cuban origin" , "one's on the floor for it" , "music one can dance to" , "Afro-Cuban or ballroom dance" , "South American dance" .)