Given that the series takes place thousands of years before the movies and books don't expect characters from the Fellowship to show up. Well, at least seven of them.
Aragorn and Boromir are both men who have normal human lifespans. Although Aragorn is a descendant of the Númenoreans, he lives a little longer than most (in the books, he dies at age 210). Still, it's a ways to go before either of them is born.
The four hobbits of the Fellowship (Frodo, Sam, Merry, and Pippin) also only live for about a hundred years, so they won't be making an appearance either.
Dwarves, such as Gimli, live for about 250-350 years, so, as with the others, he will not be popping up anywhere in The Rings of Power.
The final two members of the Fellowship—Gandalf the Wizard and Legolas the Elf—are immortal, so while it is unlikely that they will appear, we certainly can't rule anything out as the exact birthdate for both characters isn't known.
Fear not though, as there are a few characters from The Lord of the Rings trilogy that will be appearing in The Rings of Power. Most notably, Elrond and Galadriel the Elves. In the films, they were played by Hugo Weaving and Cate Blanchett, respectively. Actors Robert Aramayo and Morfydd Clark will be taking up the mantle in The Rings of Power.
Maxim Baldry will be playing Isildur, the future human King of Gondor, who, at the final battle of the War of the Last Alliance, cut the One Ring off of Sauron's hand, destroying him. As he and Elrond went to destroy the Ring in Mount Doom, Isildur succumbed to its influence and kept it for himself.
Fans outside of just the films will also see Celebrimbor, played by Charles Edwards, be a supporting character in the series. Per the official canon, Celebrimbor is the elf who helped Sauron forge the Rings of Power. So, basically, Celebrimbor helped the bad guy nearly take over the world.
Celebrimbor was a major character in the video games Middle Earth: Shadow of Mordor and its sequel Middle Earth: Shadow of War. While it's uncertain how much Celebrimbor will play into this series, it seems as if he will forge all the rings of power by the time The Rings of Power concludes. I mean, it is the name of the show after all!