Choose to back Mary, at heart a complex woman (7)
I believe the answer is:
electra
'a complex woman' is the definition.
(woman after whom the Electra Complex is named)
'choose to back mary at heart' is the wordplay.
'choose' becomes 'elect' (electing is a kind of choosing).
'to back' says the letters should be written in reverse.
'at heart' indicates the central letters.
The central letters of 'mary' are 'ar'.
'ar' in reverse letter order is 'ra'.
'elect'+'ra'='ELECTRA'
(Other definitions for electra that I've seen before include "titled lady" , "heroine of Greece" , "Agamemnon's daughter" , "Tragic daughter of Agamemnon" , "Daughter of Agamemnon and Clytemnestra (who has a complex?)" .)