A broken handle on a rolling suitcase can be a major inconvenience. However, the problem can be very easily solved by purchasing a new handle and replacing your damaged handle.
Purchase a new handle similar in size and colour to your broken one at any major luggage store or directly from the manufacturer.
Open your suitcase up, and locate the screws that keep the handle in place at the top of your suitcase.
Unscrew the handle from the inside and remove your broken handle. The old handle is not able to be repaired, so you can simply toss it out.
Place the new handle in the location needed, routing the handle part through the top end of the luggage so the handle can be accessed from the outside of the suitcase. Screw the new handle into place.
Zip your suitcase back up, and pull up on your handle to have it extend out all the way.
If your luggage is fairly new, it may still be covered by the manufacturer. In addition, if your luggage handle breaks, try contacting the manufacturer to see if they can provide you a replacement handle for no additional cost. Many companies will do this if they provide a guarantee on their product.
Your new luggage handle that you purchase must be similar, or exactly the same size, as your broken handle. Otherwise, it may not fit properly on your luggage.