While Star Trek fans are still enjoying the epic happenings in Picard, the season is already on its second half and they're already excited for what's to come following the show. It is already known that the third season of Star Trek: Discovery will be released this year, but it is possible that it could happen immediately after Picard.
The Next Generation's Jonathan Frakes has recently announced that Discovery has already wrapped filming. This led some fans to believe that new episodes from season three could arrive in as early as April. Picard's finale will drop on March 26 and since the third season is a quasi-prequel to it, Discovery could actually be released very soon.
That being said, when a project wraps production, it doesn't necessarily mean that the episodes are ready to stream. Of course, there would still be post-production involved, which may push back the speculated date even further. However, if enough episodes were filmed before October of last year when the NYCC trailer dropped, it isn't entirely impossible for the third season to premiere soon.
The debut season for Discovery was split into two chapters, so if the upcoming season will do the same, then the first part might actually arrive as early as you think. In addition, Picard broke records for CBS All Access, which will have the company opt to keep more subscribers as much as possible. Of course, one way to do that is to cater to their wants, one thing that'll keep the subscribers and possibly pull, even more, is if Discovery Season 3 could actually premiere early.
For now, fans could only wait and see if there'll be any updates on Discovery's upcoming season. In the meantime, fans could look out for Picard, which airs on Thursdays on CBS All Access.