While there are a few legacy characters from TOS they could bring in, it’s not like SNW has a shortage of characters to follow up on.
From TOS: Leila Kalomi, Garth of Izar, Dr. Mark Piper, Dr. Richard Daystrom, Kevin Riley, Thomas Leighton, and Kodos. Maybe Sulu if he’s shown to be in astrosciences at this point of his career. Maybe comms officer Alden, from WNMAGB. Maybe Janice Rand.
From The Cage: Dr. Phil Boyce, Jose Tyler, J.M. Colt, Garison
From TAS: Dr. Sarah April. Stavos Keniclius. Spock’s bullies from “Yesteryear” . Spock cousin Selek, his aunt T’Pel, and his uncle Sasak. Bem.
From DIS: Siranna, Ambassador Siobhan Tilly, L’Rell. Dennas and the House of D’ghor. Ash Tyler. Xahean leader Po. Admiral Terrel.
In addition, there are a few background characters on the USS Shenzhou from the premiere of DIS that could make a one off appearance. Ensign Jira Narwani, Shenzhou’s tactical officer who wears a tactical helmet. Dr. Nambue, Shenzhou’s CMO. Britch Weeton, the Shenzhou’s transporter chief and engineering liaison. Troy Januzzi, Shenzhou’s comms officer .
There’s a bunch of crewmebers from Pike’s Enterprise on DIS S2 that haven’t been seen again. Louvier, the chief engineer before Hemmer. Amin, the helmsman before Ortegas. Nicola, the comms officer beside Uhura. Kroad, the other science officer besides Spock. Mann and Zuniga, the tactical officers. There are also Shankar and Christina, the other comms officers besides Uhura that haven’t been seen against since SNW S1.
From Short Treks: Lynne Lucero. Thira Sidhu. Tevrin Krit, his Orion guards, and the other bounty hunters (female bounty hunter, Klingon bounty hunter) that are pursuing Harry Mudd in the Short Trek “The Escape Artist”. Maybe even Harry Mudd, the android. And also Craft, in a “Future Tense”-type of story.
From the Kelvin Movies: really just Captain Robau. Maybe a reference to Admiral Marcus and Commodore Paris. Maybe Balthazar Edison, Jessica Wolfe, and Anderson Le if there is a flashback to the ENT era.
They can even go further back to ENT. Maybe Lorian is around. Maybe Karyn Archer is around. Phlox, Feezal Phlox and those Denobula geologists should still be around. Jhamel and her daughter Talla should still be around telling stories about Shran. The female Xindi Aquatic, Kiaphet Amman’sor, theoretically should still be around. Admiral Valdore might still be around, though may contradict his fate in the ENT novels, and he’d be secretly living as a Vulcan at this point. Even Travis Mayweather should still be around; humans can live to 140 in Star Trek, and Mayweather would only be 133 during SNW S2.
Maybe Jack from ENT and Jackson Roykirk are the same person and SNW can establish that.
Maybe we see Emony Dax after she was mentioned to have met Bones on DS9.
Basically, my point is we don’t really need to see the TOS crew. There are more than enough characters to explore, that can help to flesh out the pre-TOS era.