As I see it, there's two possibilities:
- If the other new characters on Picard are popular enough, CBS might decide to basically continue the show with his crew, but without him. Obviously it means a new name, but fundamentally it might be a linear continuation - particularly if the writer's room remains untouched.
- On the other hand, they might decide to replace Picard with Star Trek: Seven of Nine or another popular Berman-era character who is still reasonably young and able to lead a 24th/25th century show.
Season 1 finale: Picard is shot after exposing the bad guy (Admiral Nechayev) who had teamed up with Romulans to hide the presence of liberated Borg drones as cannon fodder and mining slaves. The crew escape from Nechayev's Warbird by hiding in the long-thought dormant Bajoran Wormhole, where they are greeted by the Prophet Sisko.
Season 2:
Star Trek: Sisko - the crew convinces Sisko, in a trippy premiere episode, the value of humanity again, and he swallows up and destroys Nechayev's evil fleet and joins the crew after depositing them outside of Earth. Together they learn that the Nechayev conspiracy goes further than the Romulans, and involves a secret alliance of Klingons (RIP Chancellor Worf) and Cardassians. Sisko, reporting this conspiracy to Starfleet C-in-C, Fleet Admiral Riker, is destroyed by the use of the Orb of Peace, and he places one of his fellow conspirators onto the ship: former Admiral Kathryn Janeway.
Season 3:
Star Trek: Janeway - Janeway quickly reveals the plot, in private, to Annika, and the fact that she's a double agent working to take down Fleet Admiral Riker. Being sent on missions by Riker of ill-repute, she struggles with his orders and maintaining her deep cover. With the help of Dahj and Annika, Janeway discovers that Riker is actually long-dead and replaced by Tom Riker - a mole of the Cardassian Union under the auspices of Prefect Garak. She reveals this, the murder of Sisko, the entire conspiracy, and all, to Jake Sisko who publishes the record galaxy-wide.
Season 4:
Star Trek: Archer - it's the dawn of the 25th century. After exposing a massive conspiracy among four grand polities (Klingon, Romulan, Federation, Cardassian), Janeway has gone into hiding with Annika somewhere in the Delta Quadrant, and Chris Rio and his crew have to navigate the economic and societal collapse of the Alpha Quadrant powers. The Bajorans secede, followed quickly by the Andorians, Denobulans, Vulcans, and Caitians. Then an "Earthexit" vote is approved, and United Earth attempts to secede from the UFP. These developments are frowned on by a shadowy elite, who use a "time capture" to kidnap and clone UFP founding father Jonathan Archer from a speech on the cusp of his 2184 Presidency. Archer is confused and finds himself onto Rio's crew as they must fight several factions seeking to use the time clone for their own agenda in the Federation Civil War.
