One can find a replacement drill chuck in many stores that offer hardware and home improvement tools. An example of such a store is Home Depot or Lowe's.
Tighten the drill bit in the chuck.
It's the part of the drill that holds the drill bit.
chuck
A 'chuck key ' is used, there are 2-3 sizes.
a jt3 chuck is a chuck for a drill that takes a jt3 tapered arbour for fitting into lathes or pillar bench drills
The drill chuck
"chuck"
A three jaw chuck is usual.
Normally with a chuck key.
Chuck
I'm not sure I completely understand your question, but a larger chuck size on your drill will accommodate larger bits. You can find 1/2" chuck drills at Lowes.
There are two types of chuck. One clamps up by hand, twisting holder against chuck base. Others have a serrated edge and need a chuck key.