Greek goddess accepting one of her characters as mistress (7)
I believe the answer is:
hetaera
'mistress' is the definition.
(term for a mistress or courtesan)
'greek goddess accepting one of' is the wordplay.
'greek goddess' becomes 'hera' (I've seen this in another clue).
'accepting' means one lot of letters goes inside another.
'one of' becomes 'eta' (I can't explain this - if you can you should give a lot more credence to this answer).
'hera' enclosing 'eta' is 'HETAERA'.
'her characters as' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for hetaera that I've seen before include "Old pro" , "paramour" , "Courtesan" .)