Lover's wife, Greek character important, by the sound of it? (6)
I believe the answer is:
psyche
'lover's wife' is the definition.
'psyche' can be an answer for 'wife' (I have seen 'Wife of Cupid ' mean 'psyche' so perhaps 'wife' could also mean 'psyche'). I am unsure of the 'lover's' bit.
'greek character important by the sound of it?' is the wordplay.
I cannot quite see how this works, but
'character' could be 'he' (he is a kind of character) and 'he' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for psyche that I've seen before include "A beautiful girl" , "Human faculty for thought - Cupid's lover" , "Analyse" , "Soul, spirit; lover of Cupid" , "Human soul - Cupid's beloved" .)