We haven’t seen Thrawn in any of the live-action movies so far, but that doesn’t diminish the influence he’s had over the years. Timothy Zahn wrote a trilogy of books about Thrawn before they were removed from the current canon. He’s working on new Thrawn books, two of which are out now. They dive deep into the character and explore what he was like as he rose through the ranks of the Empire.
Outside the books and comics, we see Thrawn in Star Wars Rebels as a target for rebel antagonization. Ezra and Thrawn have a particular kind of conflict between them. The end of the show is pretty open-ended, so we could see more of their ongoing battle at some point.
In Thrawn: Alliances, we learn more about how Thrawn knew Anakin. When Thrawn finds someone he gets along with, he brings them up through the ranks as he did with Eli Vanto, even if it wasn’t completely what Eli wanted to do. Thrawn is smart and extremely valuable to the Empire.