There’s also the possibility for a future role in a Fantastic Beasts movie, which, depending on how you define it, would count as a Harry Potter movie.
Odds are that we’ll see that series of films finish up before we get any other films that might see the return of Harry Potter himself, though it seems clear that movies set in that world will certainly continue as long as the audience keeps going to see them.
There are expected to be three more of them after Fantastic Beasts: The Crimes of Grindelwald comes out this November, so there are several more opportunities for Harrington to find a place in the Wizarding World, and now that his responsibilities to Game of Thrones are done, he’d be free to take one if it came his way.