A hearing, or a legal hearing, was a proceeding before a body or individual with the purpose of decision making or inquiry. A hearing was generally distinguished from a trial in that it was usually shorter and often less formal. Usually the highest ranking individual without bias to the situation presided over a hearing.
When the United Federation of Planets received an extradition request, a hearing was held to determine if enough evidence existed to warrant a trial. If it was decided that sufficient evidence exists, the charged individual was turned over to the other government and then is subject to their legal system. The Bajorans handled extradition requests in a similar fashion. (TNG: "A Matter of Perspective"; DS9: "Dax")
William T. Riker was the subject of an extradition request by the Tanugan security force in 2366 when he was accused of the murder of Doctor Nel Apgar in orbit of Tanuga IV. Though initially it appeared as if Captain Jean-Luc Picard would have to grant extradition, due to the evidence, it was eventually found that the Doctor had killed himself while attempting to kill Riker. The security force subsequently dropped its request. (TNG: "A Matter of Perspective")
Jadzia Dax was the subject of an extradition request in 2369 by the government of Klaestron IV, also for murder. This case was unique in that the alleged murder was committed by the previous host of the Dax symbiont, Curzon Dax. The request was also complicated by the fact that Deep Space 9 was a Bajoran facility, and the Klaestron government had no extradition treaty with Bajor. This required the Bajoran judge, Els Renora, to hold a hearing. Eventually, an alibi for Curzon was discovered, and the request was dropped. (DS9: "Dax")
The Klingon Empire requested the extradition of Worf in 2372 for the alleged murder of 441 Klingon civilians by destroying their unarmed transport ship during a battle. The hearing, presided over by Admiral T'Lara, eventually found that the ship Worf ordered destroyed was empty, and the allegedly dead civilians had died in a separate accident. The Klingons had hoped to stop Federation aid shipments to the Cardassians over the embarrassment of the incident. (DS9: "Rules of Engagement")
One type of hearing on Starfleet vessels was a competency hearing, in which the issue was the competency of the captain to command was challenged.
During a situation that transformed the crew of the USS Enterprise into elderly individuals, Commodore Stocker challenged James T. Kirk's ability to command. Stocker asked Spock to conduct a competency hearing, which according to regulations was Spock's duty as first officer. Spock, wanting to spare Kirk the humiliation of an almost guaranteed judgment against him, suggested Sulu, a young but capable junior officer, take command. Stocker refused, saying that Sulu was too inexperienced, and that a competency hearing was mandatory. Spock conducted the competency hearing, and a reluctant Uhura and Sulu testified about Kirk's failing abilities. Kirk tried to maintain his control, but it became quite obvious that his mind was failing. He was removed from command and Commodore Stocker assumed command. (TOS: "The Deadly Years")
Sometimes hearings had hidden agendas. Captain Picard faced a competency hearing via Remmick, who was sent by Admiral Quinn, reportedly from Starfleet Command. Remmick made his report to Quinn, and told him he could find no problem on the USS Enterprise-D despite his best efforts. Quinn dismissed him and told Picard he had to be certain. He said there were problems in the Federation and that someone was trying to destroy it. (TNG: "Coming of Age")
Request for asylum
On occasion, Starfleet had requests for asylum. In those cases, the highest ranking officer in the situation held a hearing to determine if they should grant it. Captain Janeway presided over such a hearing in 2372. The USS Voyager became a courtroom for a hearing to determine if a Q (who later went by the name Quinn) had right to political asylum on Voyager. (VOY: "Death Wish")
Inquiry to assess wrongdoing
On stardate 44769.2, a dilithium chamber hatch exploded aboard the USS Enterprise-D and sabotage was suspected. The explosion coincided with news that the Romulans had gained access to information about the Enterprise's chamber, indicating that there was a spy on board. A quick investigation turned up one suspect – a Klingon exchange officer named J'Dan, but he denied any involvement. An overzealous Starfleet admiral began a witch hunt aboard the Enterprise, determined to find a conspiracy, and eventually accusing Captain Picard of treason during fact-finding hearings. (TNG: "The Drumhead")
"Captain's Log, Stardate 1329.2. On board the USS Enterprise, a ship's hearing has been convened against the transport vessel's captain. I'm becoming concerned about the almost hypnotic effect produced by the women." Captain Kirk held a fact-finding hearing to investigate the actions of Harcourt Fenton Mudd and the women whose passage to Ophiucus III he was overseeing. (TOS: "Mudd's Women")
During an official inquiry presided over by Admiral Richard Barnett, Starfleet Academy held a hearing. The charge was that Kirk entered a subroutine into the computer making it possible for him to win a simulation and accused him of cheating. The hearing was over the Kobayashi Maru test which Kirk claimed was unfair due to its no-win programming. The hearing was suddenly interrupted when word came that the Federation had received a distress call from Vulcan. Though it was recessed, as a result, Kirk was put on academic probation and grounded from space flight. It was presumably dismissed afterwards in light of Kirk's later actions. (Star Trek)
Ilon Tandro, son of a famous military figure from Klaestron IV, accused Dax – the Dax symbiont, then known as Curzon Dax – of murdering his father, and wanted to punish Jadzia Dax for the crime. His claim was based on the fact that during a civil war a coded message informed the opposing side of his father's location. Of the people who knew the location, Curzon was the only one without an alibi. An arbitration meeting was held and Commander Sisko raised the point that Jadzia and Curzon Dax were two different entities, sparking a lengthy debate. (DS9: "Dax")
Determination of rights
The Doctor completed work on a holonovel that depicted the crew of Voyager. When the holonovel was published without his permission, the issue of The Doctor's legal rights were brought into question. This resulted in a Federation tribunal to determine The Doctor's rights. Captain Janeway brought in various members of the crew as witnesses to The Doctor's claim of personhood.
In the end, the arbitrator left the decision of whether or not The Doctor was a person out of the scope of the case, but did declare that the legal definition of "artist" encompassed The Doctor, and as such The Doctor had full rights concerning the distribution of his holonovel. (VOY: "Author, Author")
"It's an interesting system of justice you have, captain. It does have its flaws however. It emphasizes procedure over substance... form over fact."
"I'm sorry if you feel it puts you at a disadvantage."
"On the contrary, I look forward to fighting on your terms."
"This is not a fight. It's the search for the truth."
"The truth must be won. I'll see you on the battlefield."
"Sorry, it's just frustrating to hear that I have no more legal standings than a replicator."
"The Doctor exhibits many of the traits we associate with a person. Intelligence, creativity, ambition, even fallibility, but are these traits real or is The Doctor merely programmed to simulate them? To be honest, I don't know. Eventually we will have to decide because the issue of holographic rights isn't going to go away, but at this time, I am not prepared to rule that The Doctor is a person under the law. However, it is obvious he is no ordinary hologram and while I can't say with certainty that he is a person I am willing to extend the legal definition of artist to include The Doctor. I therefore rule that he has the right to control his work and I'm ordering all copies of his holo-novels to be recalled immediately."
"Your Honor, a courtroom is a crucible; in it we burn away irrelevancies until we are left with a purer product: the truth, for all time."