Bungie are apparently already working on Destiny 3, at least according to leaks on Reddit. What's more, the game will include a new game mode, a bit similar to the Dark Zone in The Division, but with more purpose and less griefing in mind.
Destiny 3 will apparently lean into the hardcore elements the series possessed back during the days of the original Destiny, that were lost with Destiny 2 as Bungie aimed for a more casual audience. First steps can actually be seen in Forsaken, with the Last Wish raid and general hardcore raider tone.
According to AnonTheNine who has a long track record of leaking correct Destiny information, Destiny 3 development is already underway and it will feature a PvEvP mode that is in some manner similar to the Dark Zone in The Division. Now, Anon claims there are distinct differences though, as The Division's Dark Zone has suffered from pointless griefing, while Destiny 3's new mode will be more about teritory control, so once you get ganked, at least the killer will be able to say it's for a grand cause.
Back to the topic of regular PvE, Anon claims that Destiny 3 will be more hardcore than Forsaken, which may imply that Bungie are attempting to bring back the hardcore fans of the original game. The leaker has also stated that Chris Barrett will be taking over from Luke Smith, but the latter still has a large role in development.
There is no official announcement yet, so the game is still likely years away from release, but Anon did post a teaser containing Europa, one of the Galilean moons, hinting that a part of the game will take place there. Another leak in the same thread states that Year 3 will be an annual pass once again.
Whoever Anon turns out to be, this person has intimate knowledge of Bungie's inner workings and has been spilling info for months now and the leak hasn't been plugged by Bungie. One could start suspecting they are leaking info on purpose at this point.