Anakin SkywalkerandAhsoka Tanohave one of the most important master-apprentice relationships inStar Warsas a whole. After the Clone Wars ended, Vader believed Ahsoka was killed during Order 66. However, a glimpse into the future showed Vader otherwise years before the two would ultimately cross paths again.
InDarth Vader(2017) by Charles Soule and Giuseppe Camuncoli, Vader embarks on the task of constructing his base on Mustafar. Vader specifically chose Mustafar not because it was the site of his greatest defeat, but because he sensed a great connection to the Force there; one that could let him see visions of what the future would be.

Fortress Vader, as it became known, was specifically designed to harness that untapped power in the hopes thatVader would be able to change the pastand save Padme. However,Vader got more than he bargained for when accessing the unknown energy.
Vader Knew Ahsoka Survived Long Before The Two Would Meet Again
Darth Vader(2017) By Charles Soule And Giuseppe Camuncoli
Darth Vader#25 reveals the rewards of Vader’s arduous work, as he is finally able to open a portal to the mysterious plane to the Force. While venturing through memories of his past in an out-of-body experience, Vader is also given glimpses into the future. In particular,Vader sees an encounter with his former apprentice, Ahsoka Tano, that would not happen for years to come.This is the first timeVader learns of any indication of Ahsoka’s survival,and it is not mentioned again until the second episode of the second season ofStar Wars: Rebels, entitled “The Siege of Lothal: Part 2.”
In “The Siege of Lothal: Part 2,” Kanan Jarrus and Ezra Bridger are being hunted by a powerful Sith that they do not recognize. When the two ask Ahsoka for her help to determine who he is and how they can defeat him, Ahsoka taps into the Force to connect to the Sith, only to feel a familiar presence which leads to a horrifying discovery:Anakin is not only alive,but has turned to the dark side. Vader also senses her presence, saying that“the apprentice lives.”He goes on to report the development to Palpatine, who instructs him to track down Ahsoka.

Most Star Wars Fans Missed The Moment Anakin Failed Ahsoka, Leaving The Galaxy To Rot
Parallel stories show a stark difference between how Obi-Wan and Anakin respond to their padawans, with Anakin making all the wrong choices.
However, the events in “The Siege of Lothal” take place nearly two decades after the events ofDarth Vader, meaningVader was aware of Ahsoka’s survival the entire time and never told Palpatine.WhenVader and Ahsoka eventually do meetface-to-face in Season 2, Episodes 21 and 22 ofStar Wars: Rebels,entitled “Twilight of the Apprentice,” he tells Ahsoka the same thing he told her in his vision: that their eventual meeting was foretold.

Why Did Vader Let Ahsoka Live? There Are Multiple Possibilities
Anakin Would Never Have Left Danger Befall His Beloved Padawan
The question as to why Vader would let Ahsoka survive and not hunt her down as a surviving Jedi has a few different possible answers. AsDarth Vadertakes place on the heels ofEpisode III: Revenge of the Sithand the final scene ofStar Wars: The Clone Wars,Vader is still struggling to “kill” Anakin Skywalker.Losing Ahsoka is very fresh to him, so it’s possible he wanted to protect his former padawan in the only way he could manage at the time.
Vader’s vision also shows him an unfamiliar image of Ahsoka and not what she looked like in that moment in time or in his memory. Since Vader sees himself fighting Ahsoka, it’s possible that he deduced that hewouldtell Palpatine in the future when the timing was right and Ahsoka was stronger, giving her a fighting chance against him. Whatever the reason,Vader’s choice to withhold informationaboutAhsoka Tanolikely saved her life, showing thatAnakin Skywalkerwas very much still alive inside of Vader.

Anakin Skywalker/Darth Vader
Conceived by the will of the Force itself, Anakin Skywalker was the prophesied Chosen One, destined to bring the Force into balance. Anakin struggled to balance competing attachments to the Jedi Order and his wife Padmé Amidala, and ultimately fell to the dark side, becoming Darth Vader. For years he served as Palpatine’s right hand man, but he was ultimately redeemed by the faith of his son, Luke Skywalker. Now a Force Ghost, Anakin continues to act as an agent of balance.
Ahsoka Tano
The apprentice of Anakin Skywalker, Ahsoka Tano was an accomplished Padawan who served during the Clone Wars. Ahsoka left the Jedi after she became disillusioned with the Jedi Council, but returned to serve in the Siege of Mandalore at the end of the Clone Wars. She survived Order 66, becoming a Rebel agent during the Dark Times of the Empire’s reign, and her adventures continue in the New Republic era. Ahsoka was last seen stranded in a distant galaxy, having failed to prevent Grand Admiral Thrawn’s return.