replacing broken outside tap handle
Fixing it might be as simple as removing the screw and handle and getting a replacement from the hardware or plumbing shop.

On the other hand, there are hundreds (thousands?) of manufacturers of hose faucets (also called hose bibs, spigots, hose pipe taps, etc.) and the stem to which the handle attaches does not have a standard size or connection method. It may be splined, it may be square, it could be various sizes.

If you don't have an easy time with a replacement handle, replacing the valve is fairly simple and this site has Helpful People to lead you through it (hint- you will need to shut off the water supply to that water line).