Alys Karstark is the daughter of Harald Karstark and granddaughter of Rickard Karstark. As House Karstark is a younger cadet branch of House Stark, Alys Karstark is a distant cousin of the main Stark family.
During the course of the War of the Five Kings, Lord Rickard's other two sons Torrhen and Harrion Karstark were killed. Jaime Lannister personally killed Torrhen, leaving Rickard outraged when Catelyn Stark freed him for a prisoner exchange. Denied his vengeance as a father, Lord Rickard and his men killed two minor Lannister cousins who the Starks had also taken prisoner. King Robb Stark was disgusted that Lord Rickard would kill two unarmed and captive boys, and without his permission. Declaring it to be murder and treason, Robb sentenced Lord Rickard to death, and (as per Northern custom), personally executed Lord Rickard by beheading him with his own sword. This caused the Karstark contingent in the Northern army to abandon the war and return home. House Bolton later betrayed the Starks at the Red Wedding, slaughtering their army and killing King Robb.
As his father's last surviving son, Harald Karstark became the new head of the House. When Ned Stark's bastard son Jon Snow and Sansa Stark tried to rally the North against the Boltons, Harald was still embittered by Robb's execution of his father, so he sided against the Starks. Harald joined the Karstark army with Ramsay Bolton's main force and engaged the smaller Stark loyalist army at the Battle of the Bastards. At the last minute, a massive new army from The Vale of Arryn arrived: the Bolton forces were pinned between them and the remaining Stark army and were totally destroyed.
Lord Harald died at some point in the battle, leaving his daughter Alys Karstark as the new heir to House Karstark.
Alys is present at a council of Northern and Vale lords in Winterfell's main hall presided over by the King in the North, Jon Snow. The council discussing how to deal with the coming threat of the White Walkers, and how to deal with the fallout of the defeat of the Boltons. Sansa Stark, Snow's half-sister and advisor, suggests giving Karhold to one of the Northern lords who had been a proven ally of the Starks, but Jon dismisses this idea, as Alys wasn't to blame for Harald Karstark's actions. The argument of what to do with the surviving Karstark and Umber children goes back and forth.
Ultimately, Jon calls Alys and Ned Umber forward. They are visibly afraid that Jon will announce that he will execute them. Instead, Jon holds to his original position that he will not hold them responsible for the crimes of their fathers, and orders them to swear fealty to the Starks once again. Relieved, without hesitation Alys and Ned ceremonially kneel, draw their swords, and swear to serve Jon and the Starks. This allows Alys to retain her inheritance as the new Lady of Karhold.
Alys is also present when Jon announces his plans to leave for Dragonstone, to make an alliance with Daenerys Targaryen in order to defeat the Night King, and leave Sansa in control of the North.
Harald Karstark’s 16-year-old daughter. Proving her loyalty, Alys bends the knee to Jon Snow and in return is granted her family’s ancestral home of Karhold.