Bridgerton fans may be distraught over the departure of season one's breakout star, Regé-Jean Page, but his decision not to appear in season two doesn't necessarily mean we'll never see Simon again! Although Simon's story mostly wraps up in the first book in Julia Quinn's series of novels, he does still exist in the Bridgerton universe and appears as a minor character in the other books. The door is definitely wide open, if everyone's schedules and decisions line up, for the Duke of Hastings to appear in season three or beyond.
Like most romance novel series, the Bridgerton books are more of a loosely connected anthology than a "series" in the way you might normally think of a movie or TV series. Instead of following the same characters over a long period of time, each book centers on different characters. In this case, each of the eight Bridgerton siblings gets their own book — and, presumably, their own season. Although the previous characters are still around and make appearances, they pretty much retreat into the background once they've had their stories told.
Although Bridgerton the TV series seems to be working a little harder to integrate the other siblings' stories into each season, rather than having them be tangential characters, it's still essentially the same format. Simon and Daphne do continue to show up in the rest of the Bridgerton books, but their story is not foregrounded anymore, and their main arc is pretty much completed by the end of the first book (aka the first season).
With that being said, there's absolutely no reason that, if both Page and the show wanted and were able to make the scheduling work, Simon couldn't reappear in later seasons. He's part of the Bridgerton family now, and he does pop up from time to time in the rest of the Bridgerton books, even a decade or so after his arrival as the series's first romantic hero. If Page wanted to return, it's easy to imagine the writers finding ways to create new plots for Simon and Daphne, just as they invented new, non-book storylines for other characters in the first season (and will presumably continue to do in future seasons). It's all about what works best for both the actor and the show. But if you're lamenting never seeing the Duke of Hastings again, I wouldn't get too upset just yet!