The boys are on a humanities tour in the city, taking in arts and culture.
English department head Stewart Tagg said from New York the boys spent 45 minutes with Ms Clark, taking precedence over the Iranian foreign minister who had to wait after the meeting went over its allotted time of 30 minutes.
Ms Clark, the administrator of the United Nations Development Programme, hosted the boys in her office at No1 the United Nations Plaza, and told them about subjects including Syria, the Ebola epidemic and Eastern Europe.
During their stay in New York the boys will be attending Broadway shows, the 9/11 Memorial, Times Square and Grand Central Station.
They have watched a baseball game.
Rector Richard Hall said the aim of the trip was to give boys interested in the arts an international experience.
