。
She looks up to him as her mentor.
Literal
She [topic-は] him [object-を] mentor [as-と] is-looking-up-to.
仰ぐ literally means 'to look up at' (raising your eyes skyward) and extends naturally — as in English — to 'look up to' someone in admiration. The set phrase ~を師と仰ぐ ('look up to (someone) as one's teacher/master') is a more elevated, almost literary alternative to 尊敬する; it carries an image of disciple-and-master, of formally taking someone as one's mentor. The ~ている marks the resulting ongoing state — having taken him as her mentor, she now stands in that relation.