Greek character: shift for capital (6)
I believe the answer is:
muscat
'capital' is the definition.
(capital of Oman)
'greek character shift' is the wordplay.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'shift' becomes 'scat' (both can mean to go away or depart).
'mu'+'scat'='MUSCAT'
'for' acts as a link.
(Other definitions for muscat that I've seen before include "Sweet aromatic grape" , "Arabic port" , "Sweet fortified wine" , "Gulf port -- sweet grape" , "Type of grape and the capital of Oman" .)