Greek character hosting a dance (7)
I believe the answer is:
lambada
'dance' is the definition.
(Brazilian dance)
'greek character hosting a' is the wordplay.
'greek character' becomes 'lambda' (letter from the Greek alphabet).
'hosting' means one lot of letters goes inside another.
'lambda' enclosing 'a' is 'LAMBADA'.
(Other definitions for lambada that I've seen before include "rhythmic Latin American dance" , "Fast Brazilian dance - mad Baal (anag)" , "few steps?" , "Fast Brazilian 3 dn" , "Lively Brazilian dance" .)