。
She gave him her consent to marry.
Literal
She [topic-は] him [to-に] marriage [of-の] consent [object-を] gave.
承諾 ('consent, acceptance, agreement') is a Sino-Japanese noun for formal agreement to a proposal — used in business contracts, formal requests, and as here, marriage. Pairing it with 与える ('give,' the formal verb of giving) gives the sentence a measured, almost legal-formality feel. The construction 結婚の承諾を与える ('give consent to marriage') sounds like older or formal phrasing — a modern equivalent might use OKを出す ('give the OK') in casual speech or 結婚を承諾する as a verbal version. Marriage in Japan is legally a paperwork act (婚姻届を出す, 'submit marriage registration'), but cultural and social consent rituals carry their own significance.