There are new Einsteins. It's just that they are solving smaller pieces of the puzzle
than Einstein did.
The "next Einstein" as you put it will probably be the person who comes up with a really
sound explanation for the workings of space and time at the Planck level (very tiny, very brief)
and/or explains the physical mechanism of quantum superposition. This is the only
real mystery in Quantum Mechanics and the person who explains it will most assuredly
be as big a Rock Star as Einstein was.
Related Threads for: Why No New Einstein?: The Real Problems.