In an alternate timeline where USS Enterprise-C travelled twenty years into the future instead of finishing the Battle of Narendra III, the United Federation of Planets slowly succumbed to conquest by the Klingon Empire. (TNG episode: "Yesterday's Enterprise") Without the Federation, the Alpha Quadrant was conquered by the Dominion and its allies. The Temporal Integrity Commission considered this timeline an "aberration". (STO mission: "Temporal Ambassador")
Alteration
The alternate timeline was created when the Enterprise-C came to the year 2366 during its battle with the Romulans at Narendra III, which had formed a Kerr loop between these times. On this timeline, Tasha Yar was alive and well, and was still serving aboard the USS Enterprise-D, now a warship in the Second Federation-Klingon War, which the Federation was steadily losing.
Somehow, Enterprise-D's crewmember Guinan retained minor memories and feelings about the true timeline, and, after convincing Captain Jean-Luc Picard to send the Enterprise-C back into the rift to finish the battle, told Tasha that in the true timeline, Tasha had suferred an "empty and meaningless" death. Wanting to die for a higher cause, Tasha voluntarily went back in time with the Enterprise-C to die with dignity. (TNG episode: "Yesterday's Enterprise")
Temporal Detour
Due to Klingon weapons' fire near the rift, its destination was altered and instead of returning to 2344, the Enterprise-C travelled even further into the future, more precisely 43 years, to the year 2409. By then, the Federation had been conquered by the Klingons before the Alpha Quadrant was overrun by the Dominion. Resistance continued even after Earth was destroyed by the Breen and Betazed occupied by the Dominion. A generation of slaves grew up that never experienced the Federation firsthand.
The Tholian Assembly remained intact and its territory extended to include the Azure Nebula after a non-agression pact with the Dominion, where it operated a base. The Enterprise appeared at this site from the Kerr loop and was captured by the Tholians, its crew added to the workforce. A week after, a Tholian-licensed freighter delivered goods to the base and its captain was approached by Castillo. He and Tasha Yar convinced the captain and the alternate counterparts of Admiral T'nae and Franklin Drake to help them regain control of the Enterprise, for the Tholians would not guard a new arrival as closely. The freighter captain succeeded in releasing the Enterprise and assumed command, with Castillo, Yar and T'nae manning stations. Tholian ships intercepted the Enterprise but the 29th century starship USS Pastak appeared in time to destroy a Tholian Tarantula-class dreadnought and assisted the Enterprise in its escape. With the Tholians warded off, the Enterprise returned to the battle of 2344. The freighter captain was beamed aboard the Pastak, whose captain explained this timeline was an aberration his job was to correct. With the return of the Enterprise the timeline was restored with one alteration, Tasha Yar remaining onboard. (STO mission: "Temporal Ambassador")
New Timeline
Upon arriving, the ship, commanded by Lieutenant Richard Castillo, was able to destroy one of the attacking warbirds before being disabled and poised to be destroyed. A Romulan boarding party, however, captured the 10 survivors of the ship, Tasha and Castillo among them, and left the ship before it exploded. While in the brig of the IRW Victorious, Castillo was brutally killed and Tasha forced into a deal with the leader of the attack force, General Volskiar, into becoming his consort (effectively a prostitute) in exchange for the lives of her crew. Tasha could sense Volskiar's emotional weakness, and accepted the deal, secretly plotting to use that weakness to her advantage. (TOS novel: Vulcan's Heart)
Aftermath
Tasha was kept in Volskiar's armored compound on Romulus's surface, where it is here she befriended one of Volskiar's colleagues, Saket, and often sought emotional support during her imprisonment.
While plotting her escape, Tasha became pregnant with Volskiar's child, and eventually gave birth to the girl whom they named Sela. Tasha and Sela adored each other, and she told her fairy tales of Earth in an effort to stimulate her human side.
This was all for nought, as when Sela was four years of age, Tasha finally completed her escape plan and, wanting to take Sela with her, ultimately failed when Sela refused to leave behind the only life she knew, and Tasha was caught. Volskiar ordered her executed, but before dying, asked her friend Saket to watch over Sela. Saket kept his promise. (TNG episode: "Yesterday's Enterprise"; TNG novel: Death in Winter; TOS novel: Vulcan's Heart)