Warning! SPOILERS for The Rings of Power episodes 1 & 2After only one episode of The Lord of the Rings: The Rings of Power, the epic prologue featured at the beginning of Fellowship of the Ring has already been set up. Set during the Second Age, The Rings of Power features several notable characters who would be integral to the status quo of Middle-Earth in the Third Age, as it's known during the Lord of the Rings trilogy and the War of the Ring. To that end, the new Amazon series has already set up the epic future for the Elf captain and herald Elrond, the future Lord of Rivendell.
As seen in The Rings of Power episode 1, Galadriel is the Elf commander of the northern armies during a period of perceived peace. Believing that the significant threat of Sauron is simply in hiding and not destroyed as many others believe, Galadriel is determined to seek him out, taking on the mission to destroy the Dark Lord from her slain brother. However, the High King of the Elves Gil-galad decrees that Galadriel and her company are to be commended for their service and sent to Valinor, the Undying Lands where the Elves can live for eternity. However, Galadriel is reluctant to go while her mission is still unfinished.
Ultimately, Gil-galad's herald Elrond is the one to convince Galadriel to sail to Valinor. He accomplishes this by promising that "if but a whisper of a rumor of the threat you perceive proves true, I will not rest until it is put right." This is quite the large commitment, though it's already known that Elrond makes good on this promise during the Last Alliance of Elves and Men and the Siege of Barad-Dûr. Led by Gil-Galad and King Elendil of the Dúnedain, Elrond was part of the vast alliance that broke through the gates of Mordor to face Sauron himself (during The Fellowship of the Ring's prologue).
Not only does Elrond continue fighting Sauron until his defeat at Barad-dúr, he then becomes a key figure during the subsequent War of the Ring and the rising threat of Sauron's return years later during the Third Age, sending forth the Fellowship of the Ring from Rivendell to destroy the Dark Lord's source of power once and for all. He also had the Elves of Rivendell reforge the sword Narsil (Elendil's blade which defeated Sauron at Barad-dûr). He then gave the sword (renamed Andúril) to Aragorn, heir to the throne of Gondor, who would also marry Elrond's daughter Arwen.
Continuing to play a role in Middle-Earth until Sauron's ultimate defeat with the destruction of the One Ring, Elrond absolutely makes good on his promise to Galadriel in The Rings of Power and will certainly do more as the series continues once Galadriel's fears are proven to be true. Even though Galadriel chooses at the last moment to remain in Middle-Earth rather than enter the Undying Lands, Elrond would still go on to fight Sauron for years just as he promised he would in this first episode.