。
You'll keep your promise, won't you?
Literal
Promise [obj-を] keep-[favor-honorific-下さる]-[sentence-soft-feminine-わね].
下さる is the honorific version of くれる ('give to me, do for me'). Combined with ~て it becomes ~て下さる, a respectful 'do X for me.' The sentence-final わね (sometimes written in hiragana as わね) is stereotypically feminine — a gentle assertive わ plus confirmation ね, giving a warm 'right?' or 'isn't that so?' Typical of older women's speech and some regional or literary registers.