Millennia ago on the planet Kastria, a traitor and criminal named Eldrad is sentenced to death for his crimes, including the destruction of the barriers that have kept the solar winds at bay. The pod containing the criminal is obliterated – but his hand survives. In the present day the Fourth Doctor and Sarah Jane Smith arrive in the TARDIS in a quarry and are caught up in a quarrying explosion. Sarah is rendered unconscious but in that state makes contact with the fossilised hand, its ring alive, and this has a hypnotic effect on her. The Doctor takes her to the local hospital, where the mesmeric power of the hand becomes more complete and both Sarah and a pathologist called Dr Carter are brought under its control. Carter later dies trying to prevent the Doctor getting to Sarah and the hand.
Sarah heads for the nearest nuclear generator, the Nunton Complex, where she causes a crisis by breaking into the reactor with the hand. It seems to thrive on radiation and begins to regenerate, growing back its missing finger and moving around unaided. The head of the complex, Professor Watsonin remains at his post when the reactor goes critical, and offers the Doctor aid and advice in trying to get to Sarah. All of a sudden the radiation has been absorbed and the crisis is over. The Doctor retrieves her from the reactor, but Sarah has no memory or understanding of what she has done.
The hand now takes over a nuclear operative called Driscoll, who is manipulated into feeding the hand ever more radiation. An RAF bombing raid simply adds to the available radiation and allows Eldrad to regenerate into a fully humanoid form. It is crystalline, female and silicon-based. Eldrad uses her powers to persuade the Doctor to take her back to Kastria, saying she helped her race thrive by building the solar barriers, which were subsequently destroyed when Kastria was caught in the middle of an interstellar war.
The Doctor, Sarah and Eldrad travel to Kastria in the present time in the TARDIS – 150 million years after she left. They find a barren and frozen world, with the few signs of civilisation many floors below ground. Eldrad is caught in a series of traps left behind by King Rokon who appears in hologram form to denounce Eldrad as the destroyer of Kastria. She perishes in one trap but regenerates as a male, crazed psychopath who reveals that he created then destroyed the barriers himself after falling out with Rokon and the Kastrian leadership. When he tries to exact his revenge he finds Rokon and the other Kastrians all dead, the race banks containing the Kastrian's genetic prints destroyed, and no possibility of a new Kastrian future. Eldrad finds a recording of Rokon that explains that the species decided to all die rather live a miserable existence underground and they destroyed the race banks to prevent any descendants from being part of Eldrad's army of conquest. To prevent Eldrad now returning to Earth and conquering it instead, the Doctor destroys the tyrant by engineering a fall into an abyss – without the ring needed to regenerate ever again.
Not long after departure in the TARDIS, the Doctor is summoned back to Gallifrey and declares he cannot take Sarah with him. She has been talking about wanting to leave the TARDIS and had packed her things, but says she would like to see Gallifrey and had not really wanted to leave. The Doctor is unable to take her to his home planet and she leaves reluctantly, telling the Doctor "don't forget me".