engagement (9)
'engagement' is the definition.
(synonyms)
This is all the clue.
(Other definitions for betrothal that I've seen before include "Promise of marriage" , "Commitment" , "Engagement to marry" , "Plight" , "Promise between two people" .)
(Other definitions for ring that I've seen before include "Circus arena" , "something at the jewellery shop?" , "resonant sound" , "Sound a doorbell" , "Piece of jewellery" .)