Warning: spoilers ahead for The Rings of Power season 1The end of season 1 of The Lord of the Rings: The Rings of Power saw the forging of the fabled three Elven rings, and while more rings are sure to come in season 2, there could be a lot more rings than you expect. Lord of the Rings lore regularly references the main rings given to each race, all of which are bound to Sauron's One Ring, but those weren't the only rings written about by J. R. R. Tolkien.
Anyone familiar with The Lord of the Rings books and movies should be familiar with the three rings made be the Elves, seven rings for the Dwarf Lords, nine rings for the Kings of Men, and Sauron's One Ring, adding up to 20 total, but the show has already hinted that even more rings beyond that number could be on the way. Tolkien specified in his writing that other lesser rings were made, and while not much is known about them, The Rings of Power has already established why they could be forged in the first place.
The Lord of the Rings Specifics Many Other Magic Rings Were Made
In the season 1 finale for The Rings of Power, Galadriel says three rings needed to be made for Elves only, and that nobody else should know about them. According to Tolkien's description of the forging of the rings in The Silmarillion, the Elves made "many rings," with the help of Sauron (under the guise of Annatar, the Lord of Gifts, but they saved the fabled three rings for themselves. These three rings were not bound to the One Ring Sauron eventually forged, but Sauron siezed many other rings from the Elves and bound them to the will of the One Ring before distributing seven rings to the Dwarves and nine rings to Men.
While Gandalf knew Bilbo had found a magic ring, it didn't concern him much for many years since he figured Bilbo had stumbled upon one of many lesser rings. Since Gandalf's very existence in Middle Earth was to thwart Sauron's return to power, and he himself bore one of the three Elven rings, so he was surely more than familiar with the danger of the Rings of Power, and even if he thought Bilbo had found one of the seven or one of the nine it would have been cause for concern since those are all bound to the will of Sauron. For Gandalf to treat Bilbo's ring so flippantly it would indicate magic rings were actually relatively common, and based on the way The Rings of Power is going, that would make a lot of sense with the show's story.
Why The Rings of Power Will Have More Rings Than You Expect
In The Rings of Power, the Elves don't initially set out to make magic rings, but to gather enough mithril to supposedly bathe the Elves in light of the Silmarils and ensure their survival in Middle Earth. The rings are simply a solution to the problem created by King Durin's refusal to provide them with more mithril (with a few nudges by Sauron, posing as Halbrand). The three Elven rings Galadriel eventually has Celebrimbor forge traditionally have properties of preservation, which both Galadriel and Elrond eventually put to use in Lothlórien and Rivendell, but it's not clear if they fully satisfy Gil-Galad or Celebrimbor's concern over the fading of the Elves. Besides, now that Celebrimbor knows how to make magic rings, he's too ambitious to quickly abandon that knowledge.
A close look during the forging of the Elven rings shows a tray with many chunks of the alloy the Elven smiths use to make the rings, and there's more than enough pieces to make the seven rings for the Dwarves, the nine rings for Men (which were all initially Elven rings), plus even more. If the original goal was to forge a mithril suit, or something of that nature, for every Elf, it's possible the lesser magic rings are created to solve a similar purpose, possibly for any Eldar who don't reside near one of the three Rings of Power possessed by Galadriel, Elrond, and Celebrimbor. Granted, the show has had to compress some of the events as Tolkien wrote them to fit into a more streamlined narrative for TV, so it's possible the show takes a different direction, but Tolkien's lore and the Eldar's motivations suggest there could be a lot of magic rings floating around before long in The Lord of the Ring: The Rings of Power.