In the season 2 finale of The Mandalorian, Din Djarin was able to defeat Moff Gideon and took the Darksaber from him. Luke Skywalker made short work of the villain's fleet of Dark Troopers, and the last time we saw him, he'd been knocked out and left at the mercy of the bounty hunter.
The Book of Boba Fett revealed that Din handed Gideon over to the New Republic, while The Mandalorian's season 3 premiere mentioned that Cara Dune received quite the promotion after bringing him in.
While there's been talk of the Moff being forced to answer for his crimes at a War Tribunal, it seems there's a little uncertainty in this Galaxy Far, Far Away that it ever happened.
When we catch up with Dr. Pershing and his fellow reformed Imperials, one mentions that he heard Gideon escaped on his way to the Tribunal. Another believes that was just a cover story and he was hooked up to a Mind Flayer, suggesting no one really knows what happened to him; we can't imagine the New Republic has brainwashed him, though!
Considering the fact he was such a key player in the Empire, it's unlikely the New Republic wouldn't have publicised Gideon paying for his misdeeds, so why is there such a mystery?
Based on what else we see in this episode - you can find more details on that by clicking here - it definitely seems like Gideon might be on the loose and still pulling the strings, though it's possible whoever he answers to is actually responsible for what becomes of Pershing.
It's long been theorised that Gideon was reporting to Grand Admiral Thrawn, so The Mandalorian may well be setting the stage for Ahsoka here with subplots once meant to play out in Rangers of the New Republic.
Don't forget that Giancarlo Esposito has already confirmed he'll return in season 3 and strongly hinted at a breakout, so we're guessing that the theory Gideon escaped the New Republic is the correct one...