The United Nations announced that Naomi Watts will be their new special envoy on HIV/AIDS.
This sentence contains an error in pronoun/antecedent agreement. The antecedent, "the United Nations," is an organization; names of organizations, groups, and name brands, as well as titles of works (books, paintings, plays, musical compositions), are singular.
To correct this sentence, change the number of the referent pronoun.
The United Nations announced that Naomi Watts will be its new special envoy on HIV/AIDS.