The Lord of the Rings movies were only about one small part of a long history. The Amazon show Rings of Power is bringing that history to the screen, and a few of the characters from that show also appear in the Peter Jackson movies, thanks to the magic of immortality. Galadriel is one of the oldest living beings in Middle-earth at the time of the films, which is one of the reasons she was chosen as the voice of the opening narration.
Not all of these characters have appeared in Rings of Power in the flesh, and likely won't considering the timeline, but they are mentioned in some scenes and are an important part of some expository dialogue. Galadriel recognizes the influence her family line has had on all of Arda, not just Middle-earth, and some of the other influential figures of her time were also close relatives. The family dynamics in these three episodes alone would impress even the most stolid of Hobbits.
6 Finrod, Brother
He's never named in the show, but the credits tell us that this character is Finrod Felagund, Galadriel's older brother, and his life is an epic one that could be its own series. He founded the kingdom of Nargothrond, famous for its jeweled caves, and was the first Elf to come into contact with Men. The Ring of Barahir, an heirloom of Aragorn's family, was a gift from Finrod.
Unlike other members of the House of Finarfin, he was vocally and vehemently opposed to the Oath of Fëanor. The flashbacks in the first episode might refer to the battle in which he was taken prisoner with Beren in an attempt to recover a Silmaril who was killed by a werewolf while in captivity. He was the first Elf to be resurrected in the First Age, one of the many family members waiting for Galadriel in Valinor.
5 High King Gil-galad, Nephew Or First Cousin Once Removed
There's some scholarly debate about Gil-galad's ancestry. According to The Silmarillion, which currently stands as established canon even though it's likely a mistake, Galadriel's father had a brother named Fingolfin, and he had three sons and a daughter. Fingon was the oldest, and his only child was Gil-galad.
However, Tolkien's son made an editing error when putting together his father's work. The elder Tolkien always intended to make Gil-galad of the House of Finarfin as the son of Orodreth, Galadriel's second oldest brother. This would make him more closely related as a nephew, according to the updated information in The History of Middle-earth, Vol. XII: The Peoples of Middle-earth, The Shibboleth of Fëanor.
4 Elrond, Son-In-Law
Viewers familiar with the lore are happy to see Elrond and Galadriel in the story, but there seems to be someone missing depending on where exactly this happens in the timeline. According to the lore, Galadriel met her husband in the court of Gil-galad, and Celeborn is another figure who seems to be conspicuously absent.
Elrond marries Celebrían, the only child of Galadriel and Celeborn. This not only makes him Galadriel's son-in-law, but it means his daughter Arwen is Galadriel's granddaughter. This is why Arwen spent most of her life in Lothlorien, and Aragorn makes references to Galadriel as her caretaker when they meet in The Fellowship of the Ring.
3 Fëanor, Uncle
For those that want to pick nits, and also for the sake of accuracy, Fëanor is Galadriel's half-uncle, the only son of her grandfather's first wife Miriel. As the master craftsman who made the Silmarils, he's one of the most important figures in Arda's history but has yet to appear in any adaptation.
Fëanor was already long dead when the events of both The Rings of Power and The Lord of the Rings began, but his legacy resonated into those ages. Celembribor not only mentions the Silmarils to Elrond when they meet but has Fëanor's hammer in his possession, which is held in reverence as a sacred artifact. It's possible he has it because it's a family heirloom.
2 Celembribor, First Cousin Twice Removed
Fëanor had seven sons, and the fifth was named Curufin. Legend has it that he took after his father more than any of his siblings, not only in his physical resemblance but also in his skills and talents. His death came at the hands of his fellow Elves at the Second Kinslaying, when he and his brothers attempted to attack the kingdom of Doriath to recover a Silmaril, the same one that Finrod had died trying to help Beren recover.
His son Celembribor was now free of the Oath of his father and was able to take up residence in Nargothrond, the kingdom Finrod had built. Eventually, he took up his residence in the kingdom of Eregion, and by then his family was more interested in making nice things as opposed to fighting over them.
1 Elros, Brother-In-Law
The twin brother of Elrond, he appears in the show only as a portrait and a legend, but fans of the show understand that he is in the room in some form. The Empress Regent was correct to be suspicious of Elendil's name, as he's a direct descendent of the first Elf to choose mortality.
Despite choosing to live as a human, Elros had a long life as the first Emporer of Numenor and was instructed personally by the Maia Eönwë. His wife was a human woman, and although she's unnamed her four children were the beginning of generations of royal families. Galadriel would have been recognized as their kin, at least in the early days.