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 vaildity 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")
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")