Modern music king appearing in South Africa (3)
I believe the answer is:
ska
'modern music' is the definition.
(genre of music)
'king appearing in south africa' is the wordplay.
'king' becomes 'K' (abbreviation for king in chess).
'appearing in' is an insertion indicator.
'south africa' becomes 'SA' (abbreviation).
'k' going into 'sa' is 'SKA'.
(Other definitions for ska that I've seen before include "Jamaican music, forerunner of reggae" , "popular music" , "Jamaican music style" , "Music genre" , "Dancehall music" .)