Lynagh, 22, was rested for the November tour after starting his first three tests in the cauldron of the British & Irish Lions series.
Livewire McDermott was an ever-present in the matchday squad during the 2025 campaign until he suffered a hamstring injury that required surgery against the All Blacks in late September.
Wright suffered an ACL injury against the Springboks in August that wiped out the rest of his season and his backline running was sorely missed as the Wallabies managed only two wins from their last nine matches.
"The couple of days we have together in early January will provide a final opportunity to look back on, and to learn from, a demanding 2025 test campaign," coach Joe Schmidt said in a news release.
"It also provides a chance to complete some national testing and check in with the players from a medical perspective before they return to their Super Rugby Pacific clubs ahead of the 2026 season."
Lynagh was one of four flyhalves named in the squad along with the recalled Ben Donaldson, Tane Edmed and Carter Gordon.
Prop Massimo De Lutiis, who endured a string of injuries last season, was the only uncapped player named in the 40-strong squad.
Wallabies January camp squad:
Forwards: Allan Alaalatoa, Josh Canham, Nick Champion de Crespigny, Massimo De Lutiis, Matt Faessler, Nick Frost, Isaac Kailea, Fraser McReight, Josh Nasser, Zane Nonggorr, Brandon Paenga-Amosa, Billy Pollard, Tom Robertson, Aidan Ross, Lukhan Salakaia-Loto, Pete Samu, Darcy Swain, Carlo Tizzano, Rob Valetini, Jeremy Williams, Harry Wilson
Backs: Filipo Daugunu, Ben Donaldson, Tane Edmed, Josh Flook, Carter Gordon, Jake Gordon, Max Jorgensen, Andrew Kellaway, Ryan Lonergan, Tom Lynagh, Tate McDermott, Hunter Paisami, Dylan Pietsch, Harry Potter, Hamish Stewart, Joseph-Aukuso Suaalii, Kalani Thomas, Corey Toole, Tom Wright