What event causes a main sequence star to transition into a Red Giant phase?

Hydrogen fuel depletes in the core, causing fusion to start in a surrounding shell.

The main sequence phase, representing the longest period of a star's life, is sustained by core hydrogen fusion. When the hydrogen fuel within the very center of the core is finally exhausted, the fusion engine stalls locally in that region. Since the outward thermal pressure immediately drops in the core, gravity momentarily wins the local battle, causing the inert helium core to contract and heat up significantly. This increased temperature in the surrounding layers is sufficient to ignite hydrogen fusion in a shell surrounding the now-inert core. This new shell fusion is often highly energetic, causing the outer layers of the star to expand dramatically and cool, leading to the Red Giant phase, which is characterized by a temporary, significant imbalance where outward pressure overwhelms gravity locally.