Star Trek: Discovery shot itself in the foot when they tried to retcon the Klingon species with its first season. They changed the look of the alien race, from the long-accepted and beloved look, into a four-nostril, orc-like thing. The designs weren't bad, by any means. Nor was the makeup and special effects. They were spot-on. The problem was that no one wanted a re-design of such a beloved species.
Yet, that's exactly what happened, and it ruined the show for a lot of fans. Some liked it. Some didn't mind it. While others ate it, hated it, and kept watching. Most fans, however, hated it. It felt like a slap in the face to long-time fans of the series. Essentially they saying "What you liked wasn't good enough, we're here to fix it for you". It rubbed fans the wrong way.
Since that fateful first season, however, Star Trek has rectified the issue and brought the classic Klingon look back, essentially undoing the mistake that Discovery made. Despite that, there are some who believe that the look was good, not only that, there's room for Discovery's version of Klingons to live on.
Discovery's Marcy Chieffo, arguably the most notable actress or actor to play a Klingon on the series, recently went on the D-Con Chamber podcast; hosted by Enterprise's Dominic Keating and Connor Trinneer to talk about the decision to change up the Klingons. While on the podcast, she revealed how she views the characters she played, saying (via ScreenRant);
"I loved the idea, particularly with T’Kuvma, that they were kind of this ancient sect of Klingon houses, and that we were also kind of the outcasts"
It's an idea that's been kicked around online by fans and one that hasn't been confirmed in any real space, but many want to see it be canonized. Sadly, the Klingon re-design was so horrid that even if it was canonically the case, that they were an ancient sect of Klingons, too many fans would not be able to get past the attempt at re-designing such a classic look. They'd still reject them, and so it's best if they're left behind.
What we do not want to forget about, however, is Chieffo, who was fantastic in her time on Discovery. She can play a Klingon any time she likes, just as long as they don't look like a Lord of the Rings villain.