Is it possible to put a new Hellcat engine into a rebuilt 1968 Charger?

Sure, just need to throw money at it.

Engine runs $15,000+, then you need to do all custom electronics, guages, mounting, driveline, transmission/shift linkages, plus beef up the front and rear ends, brakes (recommended), exhaust, and about 100 other little things.

Budget at least $30,000 for a hack job, more if you want it to look nice and be reliable.

Possible but not easy. The Hellcat engine can't operate decently without computer control so the ECU and all associated sensors and wiring would have to be transplanted as well. The Hellcat produces about 1.8 hp per cubic inch; in 1968 1 hp per cubic inch was the holy grail in stock cars. Computer control makes all the difference.

It would be cheaper and easier to go and buy a new Hellcat Charger and swap the bodies.