。
She is a teacher who has just graduated from that university.
Literal
She [topic-は] that university [object-を] left just-after [genitive-の] teacher is.
大学を出る is the everyday way to say 'graduate from university' — literally 'leave the university' — and is more common in speech than the formal 卒業する. The を here is the separative を (departure point), not direct-object を: 出る takes its origin marked with を. The pattern ~たばかり ('just done X') marks a recently completed action; here it modifies 教師 through ~の, so the entire ~たばかりの clause functions as a relative-clause-style adjective: 'a just-graduated teacher.' でた is just the kana spelling of 出た.