Here's who plays the old woman on Tatooine at the end of Star Wars: The Rise of Skywalker. Directed by J.J. Abrams, who co-wrote the script with Chris Terrio, The Rise of Skywalker brought to an end both Disney's Star Wars sequel trilogy and the Skywalker saga, and so somewhat understandably things culminated on Tatooine. There was a sense of the story coming full circle as Rey looked out at the twin suns, seeing the Force Ghosts of Luke Skywalker and Leia Organa, but she also comes across an old woman who queries who she is.
The old woman only appears very briefly in The Rise of Skywalker, but she has an important role in the movie. After Rey buries Luke and Leia's lightsabers at the Lars homestead, the old woman mentions that it's been a long time since she saw anybody there, and asks who she is. It's here that leads to Rey making the announcement that she's "Rey Skywalker," claiming the family name for herself and preparing to forge a new legacy for it.
The old woman is a key part of The Rise of Skywalker's ending, even if she's only known as an unidentified Tatooine elder, but it isn't immediately clear who the actress is. The old woman on Tatooine at the end of The Rise of Skywalker is played by Ann Firbank (credited as Annie Firbank), a veteran of the screen and stage who has been acting since the 1950s. The Rise of Skywalker is arguably among her biggest ever roles, even though she only appears for such a brief moment, but audiences may also know her from Persuasion, an adaptation of the Jane Austen novel; The Scarlet Pimpernel; A Passage to India; and Anna and the King.
Firbank made her acting debut in the 1956 TV movie Without Love, and her most recent credit aside from The Rise of Skywalker was in 2019's Intrigo: Samaria. Although Firbank has had a lot of credits over the years, her appearance as the old woman on Tatooine in The Rise of Skywalker introduces her to a whole new audience, which is particularly impressive coming over 50 years into her career.
As for who the Tatooine elder is in-universe, that's a question The Rise of Skywalker isn't interested in answering. The character definitely serves a simple purpose as a one-and-done appearance within the narrative, because it's all in service of Rey Skywalker's arc, but it also wouldn't be too surprising if she was eventually revealed to be connected to the wider Star Wars canon, since so many characters tend to get backstories or used again in other media. One theory is that she is Camie Marstrap, a Tatooine native who appears in a deleted scene from A New Hope, and whom Luke Skywalker dreams of being married to in the novelization of Star Wars: The Last Jedi. If Disney did want to connect Star Wars: The Rise of Skywalker's old woman on Tatooine to canon, then that could be a way of doing it, since she lived on Tatooine and would be around the right age, but there's no hard evidence for it right now.