Dance by graduate following sport (5)
I believe the answer is:
rumba
'dance' is the definition.
(rumba is a kind of dance)
'graduate following sport' is the wordplay.
'graduate' becomes 'MBA' (Master of Business Administration degree holder).
'following' means one lot of letters go next to another.
'sport' becomes 'ru' (rugby union).
'mba' after 'ru' is 'RUMBA'.
'by' acts as a link.
(Other definitions for rumba that I've seen before include "Umbra (anag)" , "one's on the floor for it" , "Latin American dance" , "Lively Cuban dance" , "One from Cuba" .)