What event immediately triggers the contraction of the inert helium core in a star?

Answer

Exhaustion of hydrogen fuel in the core.

When hydrogen fusion ceases in the core due to fuel depletion, the outward thermal pressure ceases. Gravity then takes over, causing the inert helium ash core to contract under its immense weight.

What event immediately triggers the contraction of the inert helium core in a star?
evolutionstarFusionheliumnucleosynthesis