Zarabeth
Zarabeth was an inhabitant of the planet Sarpeidon. 

She was exiled to her planet's past by Zor Kahn because members of her family tried to kill this tyrant of her planet. She was transported to a barren Sarpeidon Ice Age by use of the Atavachron, a time portal. She was provided with weapons, food and shelter and as her punishment, and was to live out the remainder of her existence alone and unable ever to return to her time.

Spock and Leonard McCoy of the  accidentally entered Zarabeth's time era when they attempted to follow Kirk through the Atavachron. While seeking shelter in the frozen waste, they encountered her, and she led them to safety.

Suffering from loneliness, Zarabeth told Spock that they could not return to their own time, but was unaware that Spock and McCoy had not been "prepared" by the Atavachron as she was. McCoy noticed a growing attraction between Spock and Zarabeth, which had developed as a result of the Vulcan's chronologically-induced regression to the wildness of his ancestors from that time period, and had Spock seriously thinking of remaining with her. McCoy accused her of deceiving them to persuade Spock to remain behind. An emotional outburst ensued, which brought Spock back to his senses. 

Zarabeth eventually conceded to knowing only that she could never go back and sadly agreed to lead them to the portal. Spock, still reluctant to leave her behind, finally summoned the will to do so when they heard Kirk's voice. They found their way back through the door, where Spock acknowledged the painful realization that Zarabeth had been dead for 5,000 years, yet assuring McCoy that he had fully returned to the present in every sense. ()

Appendices

Background information 
Zarabeth was played by actress Mariette Hartley. She was described in script notes as, "Hers is a face of the past: pure, clean, lovely, without benefit of visible artifice."

The design of the costume for Zarabeth was influenced by the fact that Hartley was one of many Star Trek actresses whose navels – as NBC's Standards and Practices department warned Gene Roddenberry – had to be hidden. (Star Trek: The Original Series 365, p. 343)

According to deleted references from the  final draft of the script, Zarabeth was in her second year of banishment before the landing party from the Enterprise arrived on Sarpeidon; however, in the planet's corresponding "real time", Zor Kahn had been out of power for over a century since she had been removed to the past.

Apocrypha 
In the novel Yesterday's Son, it is revealed that Spock and Zarabeth had a son named Zar and that Zarabeth died seventeen years after the events of "All Our Yesterdays" as a result of falling into an ice crevasse.

External link 
 
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Sarpeidon natives