> Have a show with a mix of new and old characters.

That's exactly what Terry Matalas has been pushing. The Titan crew we're already starting to know with older characters popping up, maybe dealing with the politics of the alpha quadrant after all of this. Old characters can pop up as needed and they can go on their own new adventures too. Go to Bajor to deal with a trade dispute and Garak and Kira are there. Get orders from Admiral Janeway one episode. Have Geordi talk to his daughter sometimes. But not every week.

Please don't make Jack the captain, though? We already did the "plucky young ahole somehow becomes the captain over everyone more experienced than him" thing in ST09 and it made sense there, we don't need it here. I like Shaw as the stubborn damaged captain who's hands off, stays in his ready room or quarters when not needed so Commander Seven has most of the responsibility. Jack can be chief medical officer I guess. The other Laforge daughter can be in engineering.

Season one of this crew is now worked together and has been season by dealing with the changeling problem. Now they have to go to Deep Space 9 to get orders from Kyra because there’s still some terrorist groups running around the beat a quadrant. Season one can beat them making sure there’s no one else trying anything stupid. Season finale should be with them dealing with it  As well as character growth for Jack. They should make him an acting ensign.  There should also be some serious repercussions for the better quadrant.

 Season two things are fine. It looks like the Cardassians are Jo ining the Federation, but a civil war breaks out. It looks like the other side definitely has some heavy hitters helping them out like the Breen and maybe some old Jem Hadar, just for the heck of it. More character growth definitely lots of space battles, and even political intrigue. Some old familiar faces from deep space nine and Voyager show up to help.

 Season 3 Seven s missing. No one knows if she’s alive or not, but Jack and the rest of the ensigns takeoff on their own by borrowing the defiant. Shaw could bring the hammer down on them but he gives them cover and they go off on their own crazy mission. Turns out now that the borg want to join the Federation a lot of their old enemies have come back to try and hunt them down and seven is trying to find a home world for them. the new world is in the Delta quadrant. Janeway Tuvok and captain Harry Kim are all involved.

 Season four has them return to the beta quadrant.  Captain Ezri Dax has made first contact with a new species.  The titan shows up to do second contact stuff, and this season can actually just be a lot more fun and exploration, and it might even include cameos from Captain Boimler and his first officer Mariner. 

I think you just described Next Generation.

Sure, they didn't have any old characters in the main cast, but characters and concepts from TOS showed up all the time, especially in the early seasons. And characters like Data and Riker were meant to be direct analogs to Spock and Kirk.

As for Discovery's time jump...I think that was just to give Strange New Worlds some room to play around without stepping on another show's toes. The producers saw how popular those episodes with the Enterprise were and decided that the fans would like to literally jump ship, but they'd already invested so much in Discovery as the flagship show of the franchise that they couldn't drop it right away.

>Let me catch up with what happened the DS9 and Voyager crews, please!

Please no, not with the way these trash shows just drag up old characters for the purpose of killing them off.