The term 'BRANCH OF THE U.N.' can be represented by two crossword solutions: OLIVE (5 letters) and ILO (3 letters). OLIVE stands for the Office of Legal Affairs, which is a branch of the United Nations that provides legal advice to the organization and its member states. ILO stands for the International Labour Organization, which is a specialized agency of the United Nations that works to promote social justice and internationally recognized human and labour rights.