Yes, Mount Everest grows about 4 mm (0.16 in) to 1 cm (0.4 in) annually—driven by the ongoing collision of the Indian and Eurasian tectonic plates.
The Indian Plate pushes northward at ~5 cm/year. Crustal shortening thickens the Himalaya, uplifting Everest and its neighbors. Simultaneously, erosion (glacial, fluvial, seismic) wears the summit down. Net growth is the balance.
Everest is a dynamic feature, not a static monument. It rises as India keeps driving into Asia.