Spielberg has had many potential heirs: Joe Johnston, James Mangold, M. Night Shyamalan, J.J. Abrams, Christopher Nolan. In my view, though, the candidate who truly fits the bill is Guillermo del Toro. Granting the differences—Catholic not Jewish, Mexican not American, Gothic horror not action adventure—del Toro is, in his own way, extending a Spielbergian cinematic tradition. They even share Matthew Robbins, among others, as a writer-collaborator.
A point to be developed and defended some other time, but noting it here for now.