Greek character possessed by a dance (7)
I believe the answer is:
lambada
'dance' is the definition.
(Brazilian dance)
'greek character possessed by a' is the wordplay.
'greek character' becomes 'lambda' (letter from the Greek alphabet).
'possessed by' is an insertion indicator.
'lambda' placed around 'a' is 'LAMBADA'.
(Other definitions for lambada that I've seen before include "Erotic Brazilian dance" , "raunchy dance" , "Latin-American dance" , "Fast Brazilian dance - mad Baal (anag)" , "few steps?" .)