An arbiter (or arbitrator) was a type of mediator used in both formal and informal settings.
Many cultures had arbiters that assumed specific duties.
The Alliance had two major titles, Supreme Arbiter of the Alliance and Deputy Arbiter. (TOS novel: Engines of Destiny)
In the Klingon Empire, the Arbiter of Succession was a primary position during the Rite of Succession. (TNG episode: "Reunion")
Prime arbiter was a title given to the second-in-command of the New Thallonian Protectorate. (NF novel: After the Fall)
In the Mirror Universe, the Vulcan Mineral Syndicate also had an arbiter as one of their members. (TOS novel: Spectre)