。
She holds onto the hope that he will return.
Literal
She [topic-は] he [subject-が] [come-back-戻ってくる] [that-という] hope [object-を] heart [in-に] is-holding.
A poetic, slightly literary register. 心に抱く is an idiom for 'harbor in one's heart' — used with abstract things like 希望 ('hope'), 夢 ('dream'), 思い ('feeling'). The clause-modifier ~という marks the content of the hope. 戻ってくる combines 戻る ('return') with the directional ~てくる, describing motion toward the speaker's reference point.