Well, Everest was still taller than any other mountain, and people still knew it was there, even before its height was first known to have been measured in 1856.
If you mean what mountain had the highest measured summit height immediately before the height of Everest was first established, I think the answer is Kangchenjunga.
In 1847 Andrew Scott Waugh, then superintendent of the Great Trigonometrical Survey of India, while observing from near Darjeeling in the eastern Himalayas, calculated the height of the massif of Kangchenjunga at 28,176 feet (8590 m). At that time this far exceeded any peak yet measured, and Waugh recorded it as the world’s highest mountain (it is in fact the third highest, though the modern accepted value for its height is 28,208 feet/8598 m).
The next time the huge Survey measured a mountain higher than this it was Everest in 1856.