Greek character hosts a dance (7)
I believe the answer is:
lambada
'dance' is the definition.
(Brazilian dance)
'greek character hosts a' is the wordplay.
'greek character' becomes 'lambda' (letter from the Greek alphabet).
'hosts' is an insertion indicator (inserted letters are welcomed or hosted).
'lambda' going around 'a' is 'LAMBADA'.
(Other definitions for lambada that I've seen before include "rhythmic Latin American dance" , "sexy dance" , "Lively Brazilian dance" , "raunchy dance" , "Fast Brazilian dance - mad Baal (anag)" .)