This is so simple so I doubt make this instructable and forgot to take photos of process.
Step 1: Just Rivet It
First, make two holes in the leash overlaping the two broken parts, you can melt the heads with a ligther to avoid them fray. I used a belt puncher to make the holes.
Before put the rivets throught them I want to share one tip I used to join cloth, use pieces of bike chain as double hole washers, one from each side, then rivet it.