While you can download the expansion right now, if you have yet to sit a certain Power level in the game, you still won't be able to play it.
The expansion is now live on PS4, Xbox One and PC, so no matter which version of Destiny 2 you own, there's plenty of new content to check out (providing you already preordered the Expansion Pass for $34.99). The expansion will also add a new social space, Strikes, Crucible Maps and, of course, even more gear and weapons to help you take on the Vex. But the expansion is just part of the story. The fans have made their disappointment known on realizing that there is a major lack in Bungie's relationship with their customers and also because there is no proper end game. And for more, be sure to check out Bungie's full patch notes. You don't need to have completed the Leviathan Raid to access this, either.
On Mercury, a planet not yet visited in Destiny 2, the Vex (bad guys, to put it simply, but the Destiny 2 lore can get complicated in these things, especially when you go into the ethics of robots) have opened up a portal that stretches across time. The next update is due on the 12th of December which will provide players with Masterworks version of legendary weapons that are created to track skills, Display them and crate orbs while acquiring multiple kills.