The Enterprise has been confirmed to return for Star Trek: The Next Generation spinoff has so far avoided stepping back aboard the Enterprise, with the exception of Picard season 1's dream sequences. At a Comic-Con to promote Picard season 3, Patrick Stewart revealed that, finally, the show would return to the Enterprise. Answering a question about whether he'll sit in the captain's chair in season 3, Stewart replied "there’s more than one Enterprise and that makes it a little complicated. But we do return to the original Enterprise."
Given the spectacular Enterprise-D crash at the end of Star Trek: Generations, Stewart's statement suggests Picard season 3 may feature time travel element or a holographic simulation of the iconic starship. The mention of multiple Enterprises suggests a return for the Enterprise-E with a new Captain post-Picard or maybe even a new Enterprise. Details are thin on the ground as to how the TNG cast are reunited for Picard season 3, but the maiden voyage of a new Enterprise could bring them back together.
Picard season 2 began with Jean-Luc invited to the new Stargazer, so season 3 could have a similar opening. The new Stargazer was captained by Rios, opening the possibility that a new Enterprise could be captained by another Picard character like Seven, or maybe Raffi. However, the fact that Raffi's not in uniform in the season 3 teaser trailer suggests she's no longer with Starfleet, so it's unlikely that she'll be in the captain's chair. Here are the more likely candidates to be the new Enterprise captain in Picard season 3.
Seven
Seven's Picard season 2 ending saw her take charge of the Stargazer and help Picard negotiate with the hybrid Agnes/Borg Queen. The season 3 teaser confirms that Seven has become a fully-fledged Starfleet officer, presumably fighting back against the anti-Borg prejudice of the institution. Depending on how much time has ed since Picard season 2, it's entirely possible that, like Rios, she has been given the command of her own vessel by the start of Picard season 3.
Whether she's been given command of the Enterprise is more complex, however. It's Starfleet's flagship, and if there's underlying prejudice against Seven then it's unlikely that she'd be put in charge. Showrunner Terry Matalas has confirmed that Seven is a Commander in Picard season 3, so it's more likely that she'd be a first officer. With season 3 set to explore how Seven fits into Starfleet, a deputy role on the Enterprise could provide a compelling study of the prejudicial barriers that still prevent her from rising through the ranks.
Geordi
Nobody knows the Enterprise like Geordi La Forge, so he's an ideal candidate to make the leap from Chief Engineer to Captain. In a Picard season 1 prequel comic book, Geordi had been promoted to Commander and was overseeing the construction of the Romulan rescue fleet. He clearly survived the devastating attack on the Utopia Planitia Fleet Yards prior to Picard season 1, and maybe even earned a promotion for his efforts in rescuing the survivors.
In Star Trek: Voyager season 5, episode 6, "Timeless", Geordi was the Captain of the Galaxy class starship the USS Challenger in an alternate timeline caused by the destruction of Voyager. This timeline was reset when Kim, Chakotay, and the Doctor defied Geordi and averted Voyager's destruction. The events of this alternate Star Trek reality took place in 2390, 5 years after the attack on the Utopia Fleet Yards, backing up his potential promotion. In the teaser trailer, Geordi speaks with fondness about his days on the Enterprise, which could be read as either nostalgia or as his reason for finally taking command of the ship. Showrunner Terry Matalas has confirmed that Geordi is now Commodore La Forge, in Naval , a Commodore is a temporary commander over a collection of ships. Perhaps the Enterprise falls under his new remit.
Worf
It's already been established in Star Trek canon that Worf was Captain of the Enterprise during the Romulan rescue mission and attack on the Fleet Yards. Una McCormack's novel Star Trek: Picard: The Last Best Hope revealed that Starfleet saw Worf's promotion as a positive political move, given the historic enmity between Star Trek's Klingons and the Federation. They hoped it would send the right message to the Romulans as to their peaceful intentions.
Worf was briefly mentioned in Picard season 1, as a trusted former colleague of Jean-Luc who would not hesitate in aiding his mission to protect Soji and expose the Romulan and Federation conspiracy. He didn't elaborate on the status of Worf's Starfleet career, or on which starship he was currently serving. Despite what looks like four pips on his collar, showrunner Terry Matalas has said that Worf is not a Captain in Picard season 3. It doesn't mean that he's no longer in the captain's chair on the Enterprise, but perhaps he has a more important role elsewhere in the Federation.
Riker
In Picard season 1, Riker is no longer Titan Captain and is instead living in reserved retirement on Nepenthe with his wife Deanna and daughter Kestra. He came out of retirement to aid Picard and Soji against the Romulans in the Picard season 1 finale but hasn't been seen since. Riker is perhaps the most obvious choice to captain the Enterprise, given how many years he spent as its first officer. However, his family tragedy forced him to rethink his priorities, making it unlikely he would take on Starfleet's flagship.
However, depending on the universal threat that brings the TNG crew back together, Riker's reserved retirement status could put him back on the Enterprise. In Picard season 1, he states that he returns to duty when needed, so he could easily be called back to captain the Enterprise in Picard season 3. This reserved retirement could even set up a Picard spinoff for Riker as a consulting Starfleet officer after his stint in the Enterprise chair.
Picard
The most obvious choice to sit in the Captain's chair in Picard season 3 is Jean-Luc Picard himself. The Comic-Con talked about how Picard season 3 is essentially a final movie for the TNG cast, so it makes the most sense for iral Picard to be in the captain's chair. Picard's monologue in the teaser trailer talks of how "you're only as good as those around you." Putting him back in charge of the Enterprise after two seasons of Picard would be the perfect way to wrap up his character arc.
Star Trek: Picard has seen the former Enterprise Captain confront his Starfleet career, his mortality, and Picard's troubled childhood backstory. After this journey of exploring the character's psychology and interrogating what drives him, it's surely the perfect time for him to return to the Enterprise for one last mission. Having Jean-Luc Picard in charge of the Enterprise one last time, with his trusted crew around him would provide the perfect ending for the Star Trek: The Next Generation spinoff.