Daenerys’s paramour was played by British actor Ed Skrein in Season 3. However, he was replaced by Dutch star Michiel Huisman for Seasons 4 through 6. It's a little unclear why Skrein left. (It was suggested he left the show to do the film Transporter, but Skrein maintains it was "a lot more political than that.")
The Night King
For Seasons 4 and 5, the Night King was portrayed by actor Richard Brake. Since Season 6, however, he’s been played by Slovak actor and stuntman Vladimir Furdik — whom we've also seen in "human" form when the Children of the Forest turned him.
Aussie actor David Michael Scott actually portrayed Beric in a blink-and-you’ll-miss-it scene back in Season 1. He was later replaced by Richard Dormer who has portrayed the role since Season 3.
Freddie Stroma played Dickon Tarly in Season 6, but was cast in ABC's Time After Time and had to drop out of Thrones, so Tom Hopper and his abs stepped into the role. By the way, you might recognize Stroma as Cormac McLaggen from Harry Potter and the Half-Blood Prince.
The Three-Eyed Raven
Veteran British actor Struan Rodger played the Three-Eyed Raven very briefly at the the end of Season 4, but when the show returned for Season 5, Academy Award-nominee Max von Sydow took over the role.
Yep, the jerk who stabbed Talisa repeatedly at the Red Wedding was recast. He was played by Tom Brooke then, but was replaced by Daniel Tuite in Season 6...and now he's meat pie.
Steven Blount played Stark-loyalist Rickard Karstark in Season 1, but when the role was expanded in Season 2, he was replaced by the gray-bearded John Stahl.
When we first saw Stannis Baratheon's wife, she was played by Sarah MacKeever and was essentially a background actor in a single scene in the Season 2 premiere. Later, in Season 3, Selyse was introduced as a named character, and was recast with Tara Fitzgerald in the role.
Sweet Tommen was originally portrayed by Callum Wharry for Seasons 1 and 2. He was then replaced by Dean-Charles Chapman (who also played another character altogether, Martyn Lannister, way back in Season 3!) for Seasons 4–6.
Myrcella was originally played by Irish actor Aimee Richardson for Seasons 1 and 2. The character didn't return (onscreen) until Seasons 5 and 6, at which point the role had been recast with Nell Tiger Free.
The Mountain has actually been played by THREE different actors. In Season 1, he was portrayed by Australian actor Conan Stevens. He was replaced in Season 2 by Welsh star Ian Whyte. And since Season 4, professional strongman Hafþór Júlíus Björnsson has portrayed The Mountain.