I'm writing a series. I hope it's a long series. I hope I get to work on it for 40 years or more (I'm 46). Whether I do or not, I have one book out, two more with my editor and beta readers (those two books are closely linked), a third that I'm revising and a list of ideas in various states of development. Barring the usual things that you bar over the next several years, we're looking at at least half a dozen books that I can see from here.
Writing a series is different from writing standalone novels, which is what I've done previously. I'm taking the Terry Pratchett approach to series - a number of more-or-less interlinked stories in the same setting, with overlapping characters, places and events - rather than the typical epic fantasy one-enormous-story approach. (I recently discovered that Steven Donaldson has published the tenth, and final, Thomas Covenant novel. I started reading those when I was at high school. I don't have kids, but if I did they would probably be about the age I was then, or older, so it's taken him a generation to finish his story. George R.R. Martin is still going, with no end in sight.)
Even if you take the Terry Pratchett approach, even if you don't follow the same characters all the time and don't have one big overarching plot arc, you'll still want to tie books together. The approach I've stumbled upon is what I call Happily Never After.
That's not as negative as it sounds. It's based on the endings to fairy stories, of course: "And the Prince married the Princess, and they lived happily ever after." The wedding in a romance, or the defeat of the main boss in an adventure, draws a big line under the story and says, "Finished now."
If you're writing a series like mine, though, that moves from story to story, nothing is a final ending. And, in fact, each ending contains the seeds of the next beginning - because every time your characters achieve something, that's another thing that can cause problems for them (or someone else) later on.
I base this, like so many things, on real life. You got the promotion you were striving for? Great. But now you have more work, more responsibility, a new set of problems. You finally asked that person out? Fantastic! Welcome to your awkward first date. You're married? Terrific! Whole new set of problems there*. You've killed the main boss? Go you! Let the revisionist history/battles to fill the power vacuum/revenge attacks/resistance to the occupation begin.
We don't need to look far in our own life or in real-world politics to see that bringing something to a conclusion often just means substituting one set of problems for another. Our childhood tales tell us that when we kill the evil guy and/or marry the prince/princess our troubles are over, but it's just not so. The "all our problems will go away if we just kill this one evil guy" narrative, in particular, has proven hideously destructive (and wildly inaccurate) within the past decade.
When I got to the end of Realmgolds, the first book in the Gryphon Clerks series, I made a list of 20 problems that the resolution of that book had either created or intensified. They're enough to keep me writing for years.
The two linked books that are currently in edit/beta? The hopeful ending of the first sets up the opening problem of the second so neatly, it's as if I planned it that way.
I didn't. I didn't need to. Every solution potentially contains the seeds of the next problem, even if you don't have an overarching plot. Even if you're working within the same book, rather than a series, in fact. (Note to self: Do that more.)
* I should mention I'm happily married. Just because you have a set of problems/challenges, doesn't mean you're miserable.