。
She wants to take up a teaching position.
Literal
She [topic-は] teaching-profession [to-に] take-up [fact-of-こと] [object-を] is-wishing.
教職 ('teaching profession, the occupation of teaching') is the formal/written word — 教師の仕事 ('teacher's work') would be the everyday equivalent. ~に就く (here written ~につく) means 'to take up, assume (a position).' The frame ~ことを望む ('to wish to do X') uses こと as a nominalizer to package the verb-clause as the object of 望む — a stiffer alternative to ~たいと思う. The whole construction reads like a phrase from a CV or formal application.