A loose, split, or broken handle is hazardous; replace it with a new one from a hardware or lumber store. To remove the old handle, clamp the ax head in a vise and saw the handle close to the head. Drill holes in the wood inside the ax head, then force out the wood with an old screwdriver or chisel. Take the ax head along when you buy a new handle to ensure proper fit.
Make sure you get a hardwood wedge with the new handle.
If necessary, sand or rasp the handle to fit the ax head; the fit should be tight. Drive the wedge into the slit in
the handle by placing a board against the wedge and hammering it. Saw and sand the handle flush with the head. Finally, smooth the handle with fine sandpaper, and apply linseed oil with a soft cloth.
Sledge and maul handles are replaced in the same way, except they may require one or two steel wedges hammered into the wooden wedge.