In your case, it also sounds as if the subject you study is not really your passion...of course, a sensible choice is important, and one should not take the most exotic of all subjects because it might make a career difficult, what motivates me is the knowledge of WHY I am studying the...
I think it is very very important to show interest in the work of the UN from day one of your university time. The competition is very high, and internships and volunteering are a good way to show what you want!