Hurin — The Sniffer From Shienar
Hurin helps track the Horn of Valere after it's stolen by Padan Fain. While some missing book moments are likely to occur in The Wheel of Time season 3, nothing involving the Sniffer, Hurin, falls into that category. In the book series, Hurin is part of the team sent to track down the Horn of Valere after it's stolen by Padan Fain. Hurin is an important part of tracking the Horn because his ability to smell violence helps them stay on Fain's trail. However, The Wheel of Time season 2 used Elyas Machera in this role, opting to remove Hurin from the show altogether.
Horn of Valere in Wheel of Time season 2
Considering the minimal role Hurin plays after helping track the Horn, it now seems highly unlikely that he will appear in the show at all. Hurin does pop back up occasionally later on in the book series, but he plays an extremely minimal role. Further, it's easy for the show to use Elyas or Perrin's wolfbrother abilities to fill in for Hurin's Sniffing, making it even more unlikely that Hurin will ever appear on-screen.
Ingtar riding a horse in Wheel of Time season 2.
Aginor — Forsaken Member
Aginor, a member of The Wheel of Time's Forsaken, would likely have appeared in season 1 if he were to be included in the TV series, but his continued absence in season 2 seemingly confirms that he will be one of the Forsaken cut from the show's continuity. It's widely believed that several Forsaken will ultimately be left out of the show due to time restraints, and Aginor's absence from season 2 makes it highly likely that he is not part of the show's plans. In the books, Aginor is killed at the Eye of the World before being resurrected by the Dark One in a new body.
An illustration of Aginor from The Wheel of Time frowning.
When this storyline was cut from The Wheel of Time season 1, it already seemed likely that Aginor would not appear in the show at all. However, now that season 2 has introduced two more Forsaken and set up several others without mentioning Aginor, it's all but confirmed that he will remain absent from the series. Anything is possible, but if Aginor were to be part of Prime Video's plans, it feels like he would've been shown or mentioned by now.
Fares Fares and Natasha O'Keeffe as Ishamael and Lanfear in The Wheel of Time season 2
Balthamel — Forsaken Member
Much like Aginor, Balthamel is a Forsaken member who would likely have appeared by now if he were part of the show's plans. He is also present at the Eye of the World in the first Wheel of Time book, and like Aginor, he is killed there and later resurrected by the Dark One. Balthamel is one of the less impactful members of the Forsaken, so it makes sense that he would be one of the villains who gets cut. Further, the show has taken time to set up several new Forsaken members other than him, making it even more likely that he will never appear in the show.
An illustration of Balthamel smiling in The Wheel of Time.