Game of Thrones and the Harry Potter franchise share a total of nine cast members, starting with Michelle Fairley, who plays Catelyn Stark in GoT, and who also appears as Mrs. Granger in Harry Potter and the Deathly Hallows.
Grand Maester Pycelle in GoT was played by Julian Glover, who was also the voice of Aragog in the Harry Potter movies.
Nymphadora Tonks in Harry Potter was played by the same actress who played Osha in GoT named Natalia Tena.
Although there are several others, these are the most prominent roles of the joint cast members.