Psychokinesis or telekinesis is an ability to move objects using only the mind.
After being exposed to the affects of the galactic barrier in 2265, Lieutenant Commander Gary Mitchell and Doctor Elizabeth Dehner developed many special abilities, including psychokinesis. (TOS episode: "Where No Man Has Gone Before")
The psychokinetic humanoid Garda lived in the jungles on Bira III. With their mental abilities, they were able to build 12-story-tall Mayan-like stepped pyramids and other structures. Led by Netuya, they also were able to hold their own during civil wars against the technologically-superior Stoyak, a competing humanoid race on the planet. (TOS comic: "A World Against Itself")
Using psychokinesis, the Arivne species created a microstar out of a black hole, and were able to continually refuel the elements the star uses to warm the rogue planet of Anomaly. They were also capable of shutting down nearby technology that caused them psychic irritation, even if such influence violated the laws of physics. In 2269, they transported a landing party from Anomaly to the starship USS Enterprise while it was traveling at warp to the Academy planet.
In 2269, Irapina used psychokinesis to transport three members of their species to Federation space from a fleet of Irapina starships 25,000 light years away. The effort expended so much energy that it slowed their travel to the Federation by a century. (TOS novel: Planet of Judgment)
Some Vulcans had, or were able to develop, psychokinetic abilities, notably the six female priestesses who assisted High Priestess T'Lar during Spock's Fal-tor-pan ceremony. Prior to the ceremony, they telekinetically carried Spock's body up Mount Seleya to the temple at the top. (TOS movie: The Search for Spock)