The short answer is: nobody knows right now.
However, as of February 2022, Peloton has an FAQ on this topic on the Peloton Homecoming website. There, they say that the Peloton Studio in New York Studio is slated to open in Summer 2022. The Peloton London Studio is also scheduled to open at the same time. Of course, this schedule could shift & change.
Peloton closed their studio to the public for classes on March 14th, 2020. It has remained closed ever since then. As various health restrictions have been lifted, many people have been wondering when the studio will reopen so people can sign up and take classes in person with their favorite coaches.
Peloton has stayed quiet on the subject, providing no guidance. They have simply said there is no set in stone date for the Peloton studio to reopen. It's likely Peloton will proceed very cautiously - although visiting the studio is a great experience for those who can, and also helps provide some extra energy for instructors to feed off - at the end of the day, there are millions of members worldwide who all take the classes remotely.
We will be sure to update this article once more information is available.