Woman takes engagement rings back (5)
I believe the answer is:
agnes
'woman' is the definition.
'takes engagement rings back' is the wordplay.
'rings' indicates the answer is hidden within the clue (in the sense of encircling/enclosing).
'back' is a reversal indicator.
'senga' can be found hidden inside 'takes engagement'.
'senga' written backwards gives 'AGNES'.
(Other definitions for agnes that I've seen before include "Scandinavian singer" , "girl" , "Miss Grey" , "The Eve of St. - (Keats)" , "Girl's name" .)