How does a star evolve after it exhausts the hydrogen fuel in its core?

It begins fusing heavier elements like helium into carbon and oxygen

When a star runs out of hydrogen in its core, the balance between gravity and internal pressure is disrupted, causing the core to contract. This contraction significantly increases the core temperature, which allows the star to begin the fusion of heavier elements, specifically transitioning from burning hydrogen to burning helium, and subsequently producing elements like carbon and oxygen. This progression signifies the aging of the star, often leading to it expanding into a red giant. This cycle of changing fuels continues until the star can no longer generate enough outward pressure to counteract the crushing force of gravity.