AU where Jason still does the Red Hood thing, but he specifically shows up when Bruce is in a different country on WE business, Tim is in California with Young Justice, and Dick is on a space mission. This means that at first some people just assume he’s the vigilante that Batman left in charge, before they’re like “ohhhhh, he’s being a crime lord. Okay, yeah, maybe this isn’t sanctioned,” and also he said something about the Bat that sounded SUPER bitter, and not in a “he’s making me take care of Gotham” way
But Gordon is a good detective, so he makes sure to do his research and realizes hey, crime has actually gone down under Red Hood’s rule, and figures “fuck it” and approaches him like “hey, you’re doing a decent job, also here’s a list of cops I’m pretty sure are involved in the mob but I can’t prove it, have fun” and Jason is just like “thank you for the enrichment :)” and two days later half of the people on the list are dead, a quarter have had their personal files leaked to the FBI, and the others have all been given the all-clear via a folder left on the roof of the GCPD headquarters.
Anyway, Jason ends up putting the red bat on his armor not to piss Bruce off (even though that was the original plan), but because he’s become the same symbol of hope as the light shining in the sky, just focused specifically on the long-forgotten East End, specifically Crime Alley. The people love him, Gordon doesn’t really give a shit that he sometimes kills people (he’s been praying for the Joker’s downfall for years now), and it’s the most peaceful the city has been without Batman literally ever.
Bruce comes back full of anxiety and expecting the city to have imploded or sunk into the sea, only to find that… it’s fine. In fact, it’s doing better than average. No rogues are running rampant, crime is down, and when the Bat Signal turns on, instead of the yellow that it’s been for years, it’s glowing blood red (one of the rookies put a filter on it since the normal Bat was still out of town).
He gets to the roof of the GCPD to find Gordon already talking to someone, a man his size with a red bat on his chest and practically dripping in guns. He takes one glance at Batman and leaves, taking a folder with him.
Basically, Jason originally intends to use their absence to cement himself without having to worry about the Bats, but instead accidentally starts to replace him. Bruce is crashing out. Dick is still in space. Tim is in the middle of murdering Santa Claus. Jason, on the other hand, has convinced Gordon to have an active shoot-on-sight order for any time the Joker escapes, and is living his best life