My favorite original series Star Trek episode, "The Gamesters of Triskelion," deals with slavery. Three members of the crew become gladiatorial slaves on a mysterious planet. Although the gamesters use the word "thrall" (the native Anglo-Saxon-derived English synonym), many narrative tropes about slavery are involved: slave collars, slave auctions, and sexual domination.
From the Wikipedia plot summary:
The Federation starship Enterprise is on a routine inspection of an unmanned station at Gamma II. Captain Kirk, Communications Officer Lt. Uhura and navigator Ensign Chekov attempt to transport, but disappear before the system is activated. Observing no signs of life from the station, Commander Spock orders a system-wide search for their missing crew members. No trace of them is found, but Spock discovers a faint ion trail, and orders the ship to follow it despite the protests of Chief Medical Officer Dr. McCoy, and Chief Engineer Scott.
Meanwhile, Kirk, Uhura, and Chekov find themselves in a gladiator arena on a strange planet. They are attacked by four humanoids and defend themselves for a time but are finally subdued. A humanoid calling himself Galt, Master Thrall of Triskelion, informs the three they are to be trained to participate in games to entertain his masters, the Providers. Each is fitted with a "collar of obedience" that engages when they disobey the Master Thrall's orders. Uhura, Chekov, and Kirk are assigned individual "drill thralls": Lars, Tamoon, and Shahna, respectively; Uhura and Chekov do not get along comfortably with their instructors, but Kirk develops a rapport with Shahna. After a period of training, the Providers bid for the new thralls in their currency, "quatloos".
During a run among ancient ruins outside the arena complex, Kirk tries to gain information about the Providers from Shahna, but her collar is activated when she begins to speak too freely. Kirk protests that he should have been the one punished, and when they are returned to their cells, Shahna expresses her appreciation for this. When she moves to embrace him, Kirk knocks her unconscious, and uses her key to free himself, Uhura, and Chekov, but they are stopped by Galt.