Mount Everest was a mountain on Earth, part of the Himalayas.
In 2152, Trip Tucker recalled standing on an asteroid crater twice as high as Everest to Zho'Kaan while they were stranded on a moon together. (ENT: "Dawn")
Gideon Seyetik believed Da Vinci Falls on Blue Horizon to be the same height as Everest. (DS9: "Second Sight")
In the Julian Bashir, Secret Agent holoprogram, Everest was the location of Hippocrates Noah's hideaway. It was on the southeastern slope at an elevation of twenty-five thousand feet. Noah had it built there, as he planned to flood the Earth and start the Human race anew. (DS9: "Our Man Bashir")
In 3190, Lieutenant Sylvia Tilly remarked to Captain Saru that they had an "Everest-sized mountain of data" from a gravitational anomaly to analyze. She then had to explain to Saru what Everest was. (DIS: "Anomaly (DIS)")
Mount Everest was referenced in the final draft script of ENT: "Terra Prime", as it stated, "Conditions on partially terraformed Mars are the equivalent of being half a mile higher than Mount Everest."
Mount Everest, according to the Star Trek Encyclopedia, 4th ed., vol. 1, p. 253, was located in eastern Nepal and measured approximately 8,800 meters high.