A new country has formed and voting is taking place on whether to admit this country to the United Nations. What UN organ would vote on this?

Membership in the Organization, in accordance with the Charter of the United Nations, "is open to all peace-loving States that accept the obligations contained in the United Nations Charter and, in the judgment of the Organization, are able to carry out these obligations". States are admitted to membership in the United Nations by decision of the General Assembly upon the recommendation of the Security Council.