Which this happens, you generally have limited choices for repair: (1) you can try to find a modern leather reproduction (and pay very high prices!), or (2) try to fit a modern plastic handle on the case (which never quite looks right, or fits the existing holes), or (3) you don't replace the handle and from this point on carry your case much like you would carry a sack of cement (with two hands).
This instructable is about a 4th option, which is repairing the handle you already have.
Step 1: The problem with leather handles
The strip of leather that attaches the handle to the d-rings can carry a lot of weight, and over time the leather fibers begin to deteriorate until the leather tears, as shown in the photo.
Step 2: Take apart the handle
At the top of the photo is what remained of the thin leather cover from the outside of this handle.