Where a handbrake cable attaches to an operating lever, it is usually connected via a special pin called a clevis pin. This fits through a small yoke (Y-shaped end) on the cable and through a hole in the operating lever. The clevis pin is secured in place by a split pin.
When replacing the handbrake cable always examine the clevis pins for signs of wear grooves. If you find any, fit new clevis pins. Don't forget to fit a new split pin to each of the clevis pins — if one pin falls out the handbrake will be put out of action.