I wrote this from inside the exact transition you're navigating, not from a theory I read somewhere. I climbed from executive assistant to Executive Partner to Chief of Staff myself, and I'm still doing this work today: as Chief of Staff at Pioneer Outsourcing BPO, and as fractional Chief of Staff to Epena Law, a pan-African corporate law firm.
One thing worth saying plainly before you start. Becoming a Chief of Staff is not a promotion in the way people usually mean that word, and staying an EA is not settling. They're different roles built on different skills, and there are excellent, well paid, deeply respected careers in both.