Yes this can be achieved. The replacement chuck must be the same capacity as the original chuck.
Motors and transmissions are designed to handle a specific maximum load.
Replacing a 3/8" chuck with a 1/2"(13mm) chuck is not recommended.
Make sure when you buy your replacement chuck, that you buy a chuck for the spindle size of your drill. Most drills are either 3/8"-24(10mm) or 1/2"-20(13mm).