Some articles said that the rector's appointment would mean that all of the staff of the Vaganova's contracts would expire and be up to the rector to renew. So ... they can agree to this appointment, or be dismissed, or resign.
Appointment as in nomination? Then, that sounds like a sentence Orwell could have written. If it means approved appointment, then if they don't approve he would have nothing to say about their contracts, unless the next approved Rector was a puppet. If they don't succeed in blocking his approval, then he could retaliate by refusing to renew their contracts.
Vera Dorofeeva resigned, so the articles (I can't find them now) say that all contracts have thus expired and are up to the incoming rector (Tsiskaridze) to renew or terminate. So basically ... they're already fired unless they approve.