trusteeship

1. The position or function of a trustee.
2. 1. Administration of a territory by a country or countries so commissioned by the United Nations.
   2. See trust territory.

Now largely defunct, trusteeship was the system by which the United Nations, at its inception, appointed states to administer territories whose peoples, while regarded as units of self-determination, were deemed unfit to exercise immediate territorial sovereignty. United Nations trusteeships replaced League of Nations mandates, providing a means by which administrative authority over the colonies of powers defeated in the two World Wars could be transferred to the victors without compromising their democratic and anti-imperialist pretensions. The UN Trusteeship Council, under the authority of the General Assembly, had the power to issue questionnaires and demand reports from states administering trust territories, to send missions to such territories, and to receive petitions from their inhabitants. Up to independence, all or part of the territory of Rwanda, Burundi, Tanzania, Togoland, the Cameroons, Nauru, and Somalia was ruled under trusteeship agreements by former colonial powers and the United States.

— Charles Jones

The noun has one meaning:

Meaning #1: a dependent country; administered by a country under the supervision of the United Nations
  Synonym: trust territory