Dance composed by business graduate after game (5)
I believe the answer is:
rumba
'dance' is the definition.
(I know that rumba is a type of dance)
'business graduate after game' is the wordplay.
'business graduate' becomes 'MBA' (Master of Business Administration degree).
'after' says to put letters next to each other.
'game' becomes 'RU' (rugby union).
'mba' put after 'ru' is 'RUMBA'.
'composed by' is the link.
(Other definitions for rumba that I've seen before include "Lively Cuban dance" , "Latin beat" , "What to perform" , "Ballroom dance of Cuban origin" , "Caribbean dance" .)