What I think could happen:
-Return of Narek, Narissa, and Commodore Oh. I thought they were all solid villains.
-Return of Zhaban and Laris. Don't get why they didn't go with Picard on his mission in the first place. They would've been very useful.
-More TNG characters. It's not enough to name drop them, it would be great to have them all guest star at some point. There might be some Stargazer characters in the mix as well.
-Seeing the Enterprise. Whether it's the Enterprise-E or Enterprise-F, or even an Enterprise-G, I'm imagining it will be in the second season. I'm not sold on the idea that the Enterprise-F would be an Odyssey-class vessel, with ST: Picard not adhering to Star Trek Online. Yes, an Odyssey was in the prequel comic, years too soon, but I think that was more for the fans than the series' creators making a commitment.
-I see some other Voyager characters appearing more so than DS9 characters, especially if Seven is a regular cast member. That being said, I would like to learn more about DS9's crew. It would be great to see the O'Briens, Jake, or Quark who I think might be the easiest to fit into the story. Heck, Jake could've been the reporter in the first season.
-The Doctor would be great to have on the series. Did the ban on synthetic life also mean holograms?
-Lore. Come on, why are they so skittish about bringing this character back? I was so hoping that Alton was Lore. Lore would be a great big bad for Season 2, someone who has another personal connection.
-Section 31. They were strangely absent during the first season.
-More explanation of what's happening with the Romulans. Is the Romulan Star Empire destroyed entirely, and it's just the Free State? Either way, this is ripe for storytelling.
-What about the Klingons, Tholians, Gorn, Remans, and Kzinti? With Riker mentioning them, it's time to see them again.
-I doubt it, but I would like to see more about these synthetic life forms that are just waiting out there to destroy all organic life.