What condition triggers the onset of the red giant transition for a Sun-like star?

Answer

The hydrogen fuel supply in the core becomes completely exhausted

The stable life ends when the hydrogen fuel in the core is used up, leaving an inert helium ash. This stops fusion in that central region because conditions are insufficient to start the triple-alpha process.

What condition triggers the onset of the red giant transition for a Sun-like star?
astronomystarstellar evolutionmain-sequencered giant