Master in business initially game for a dance (5)
I believe the answer is:
rumba
'a dance' is the definition.
(rumba is a kind of dance)
'master in business initially game' is the wordplay.
'master in business' becomes 'mba' ('MBA' can be a synonym of 'master in business').
'initially' means one lot of letters go next to another.
'game' becomes 'ru' (rugby union).
'mba' after 'ru' is 'RUMBA'.
'for' is the link.
(Other definitions for rumba that I've seen before include "Afro-Cuban or ballroom dance" , "Latin American dance" , "One from Cuba" , "Strictly round" , "South American dance" .)