When a high-mass main sequence star runs out of both hydrogen and helium in its core, the core begins to fuse

The core beings to fuse carbon into heavier elements.

Explanation:

As the star runs out of hydrogen and helium, the energy production in the core stops, and there isn't enough outward pressure to hold the star up. The start contracts, and this heats up the core (pressure increases, temperature increases)  creating temperatures high enough to fuse carbon into heavier elements like oxygen, silicon, neon, sulfur, magnesium, and iron.

But a star can sustain itself on Carbon fusion only for so long. In about 600 years (how long exactly depends on the star ) the star runs out of carbon and what happens next depends on the mass of the star; the star either collapses into a neutron star, or begins fusion heavier elements like neon.