。
She's an English teacher fresh out of college.
Literal
She [topic-は] college [object-を] just-graduated [genitive-の] English [genitive-の] teacher is.
Two patterns. 大学を出る is a colloquial alternative to 大学を卒業する ('graduate from college'), literally 'leave college'; を marks the institution being departed. ~たばかり is the 'just done' construction — attached to a past form, expressing recency. Here the whole clause 大学を出たばかり ('just graduated college') functions as a relative-clause modifier of 英語の先生 — 'an English teacher who has just graduated college.'