Is the a higher unclimbable mountain than Everest?

Yes, Mauna Kea is a higher unclimbable mountain than Mount Everest.

Mount Everest's summit is 8,848.86 m (29,031.7 ft) above sea level, making it the world's highest mountain.

Mauna Kea is a dormant volcano on the island of Hawaii. While Mauna Kea's summit is only 4,205 m (13,796 ft) above sea level, its base is 6,000 m (19,685 ft) below sea level, making its total height approximately 10,205 m (33,480 ft), measured from its base on the ocean floor to its summit.