Most of us here have probably heard of, and maybe even watched (some of), Amazon's new series set in Tolkien's universe. And while we may have differing opinions on whether it's good or bad (personally I think it's been decent so far, though I find the Harfoot people to be a bit annoying), I wanted to dive into something with it.
And that's the "extension of a setting". The idea is that what's been written down already can be expanded upon, one way or another.
Some people seem to believe that the vision created by an author or an artist is the only correct one. But for most creators that isn't the case. Art and literature is experienced through the lens of the reader and the onlooker. It cannot be what it is without the audience, and this is also why we may experience and like different things. For the most part, creators would LOVE for you to build upon their creations, even if you cannot legally release that creation to the world — they still very much want you to do so at home.
I should preface that with the fact that we don't know where in the Dragonlance Timeline the new setting will take place, but we DO know where the old ones took place.
So, the Hobbit and the Lord of the Rings books take place in the Third Age (the Age of Arda) but even by the mere name, you can hear that there are two more ages to explore (which the Rings of Power series is doing by exploring the end of the Second Age, and likely the beginning of the Third Age) for the enterprising GM, leaving plenty of room for you to explore. Because when you think about it, apart from the Silmarillion, the books by Tolkien take place in less than a single century, during an age that spanned three millennia. So why should the heroes of your Campaign be overshadowed by the canonical ones? At least around your gaming table, YOUR heroes should be the main focus of the story, not the heroes that belong to someone else.
Whether that then means you put your story many years before, or many years after is up to you, but you should definitely embrace this trend so that the heroes that the players bring to the table are the main focus of the story.
Dragonlance again suffers a little bit from this, but on a more condensed timeline, as the history of the world is shorter, but has been explored with more books than Middle-earth has. Most of the campaigns take place during the Age of Despair, where the Heroes of the Lance finally defeat the evil hordes. But there are several deliberate holes left in that story. The Heroes of the Lance defeat the Dragonlady (technically Kitiara was also the Blue Dragonlord) as well as Lord Soth, but several other big threats are never addressed, such as the White and Green Dragonlords or one of their many Highmasters (the direct servants of the Dragonlords).
But even the Age of Despair is only about 300 years. It's possible to explore the rise and fall of Ishtar in the Age of Might, and thousands of years to explore in the Age of Dreams — or perhaps the one that came after the Age of Despair: The Age of Mortals.
So, for Dragonlance this is practically baked in that you're encouraged to explore other Ages within a world and deviate from the canon, because so much of it is left undescribed, as nothing more than a timeline to work from.
In short, go forth and make the worlds your own!