Starfleet isn’t a military organization but it’s run like one, and it follows a code of justice with various penalties for breaking the law. When necessary, a person can be imprisoned in a ship’s brig for things like murder or other high crimes. Normally, Starfleet and the Federation don’t have a death penalty, but there was at one point a single law that allegedly required it if that law was broken.
This was General Order 7, which stated, “No vessel under any condition, emergency or otherwise, is to visit Talos IV.” Should any member of Starfleet travel to, land upon, or visit with the inhabitants of Talos IV, that person was potentially subject to execution. The threat posed to Starfleet stemmed from the Talosians’ psychic abilities, which enabled total mind control, implanted hallucinations, and more.
Much of the regulation was classified and known only to senior staff, while everyone in Starfleet was aware that travel to the planet was prohibited. The USS Enterprise, commanded by Captain Pike, visited Talos IV in 2254, and several ships, including the USS Discovery, visited the planet in later years, though there’s no record of anyone being executed for violating General Order 7. Since the capital punishment element of it was mentioned by a Starfleet officer who turned out to be a Talosian illusion, it’s possible that no one ever has or will.
