？
She works for a government agency, doesn't she?
Literal
She [topic-は] government-agency [at-に] is-working [right?-のでしょう]?
政府機関 (せいふきかん) means 'government agency' — 政府 (government) + 機関 (institution/agency). 勤めている means 'is employed at.' The のでしょう？ at the end combines の (explanatory) with でしょう (probably), forming a tag question: 'she does, right?' or 'isn't that so?' It seeks confirmation rather than new information.