The Rings of Power has scrambled The Lord of the Rings timeline pretty thoroughly, but Elrond is likely around 1755 years old at the time of the show.
The Lord of the Rings: The Rings of Power is set thousands of years before The Lord of the Rings story most of us know, the one with Frodo and Gollum and the journey of the One Ring from the Shire to Mordor; that story takes place during the Third Age of Middle-earth while The Rings of Power is set during the Second. J.R.R. Tolkien created a very detailed timeline of events in his invested fantasy world; it goes all the way back to the creation of Arda, on which Middle-earth is only one continent. Some of the immortal elven characters, including Elrond, have been alive for a very long time.
So how old is Elrond exactly? Well, we know he was born in the year 532 of the First Age, when Sauron’s boss Morgoth fought the elves over the sacred Silmaril jewels. The First Age ends with Morgoth’s defeat in the 590, whereupon the calendar resets back to 0 for the Second Age. Elrond is just 58 years old at this time.
The Second Age of Middle-earth is documented in the appendices to The Lord of the Rings books and in The Silmarillion. That said, the show scrambles Tolkien’s timeline pretty hard; events that take place over a thousand years apart by Tolkien’s reckoning happen simultaneously on The Rings of Power, so it’s difficult to drill down and figure out Elron’s exact age.
It’s not clear how much further The Rings of Power might scramble things by the end. In Tolkien’s book, the Second Age lasts for 3,441 years, but the show is collapsing things down to make it look more like the major events are playing out over the course of several years. However confusing the timeline, you can rest assured in the knowledge that Elrond is very very old.