An arbiter (also called arbitrator) was a person who mediated disputes. Depending on the culture or legal system, this may occur in or out of court, or in a formal arbitration hearing. Some used the term synonymously with judge.
Data was selected by Captain Jean-Luc Picard and the individual purporting to be Ardra as an arbitrator in 2367 to decide the validity of the Contract of Ardra. Data initially requested that Picard reject him as an arbitrator, as he could not guarantee a verdict in Picard's favor, but he accepted that and noted to Data, "you'll make a fine judge." (TNG: "Devil's Due")
Els Renora served as an arbiter of the Klaestron's demand to extradite Jadzia Dax in 2369. (DS9: "Dax")
Benjamin Sisko served as arbitrator over the case of Rugal, the Cardassian war orphan, who had been brought up by Bajorans. (DS9: "Cardassians")
Odo intended to bring Quark in front of an arbiter for smuggling kemacite. (DS9: "Little Green Men")
Several months later, an arbiter on Deep Space 9 sentenced Ojuy Gel to three weeks of community service on sanitation duty. (DS9: "Crossfire")
In 2374, an enraged Dukat angrily called Benjamin Sisko "the supreme arbiter of right and wrong in the universe." (DS9: "Waltz")
A Federation arbiter was appointed, in 2378, to hear the case regarding The Doctor's rights to control his own work. It was found that, although the arbiter was not prepared to rule The Doctor a person, he fulfilled the definition of an artist under the law and as such, had the right to control his own creation. (VOY: "Author, Author")
In approximately 3074, The Doctor's EMH backup module wondered what would happen to him if he were found guilty of the crimes attributed to him in the holoprogram The Voyager Encounter. The Emergency Medical Android was depicted as designing the bioweapons that killed eight million Kyrians. According to Quarren, the penalty would be severe, but it was up to the arbiters. The Doctor's program could be decompiled. (VOY: "Living Witness")