Detach wire infill material from the fence posts between the stretched area and the nearest corner post by pulling out the staples that hold it in place, using fencing pliers.
Instruct an assistant to grasp the free end of the detached fencing material by placing the hooks of a fence stretcher onto a vertical strand of wire just past the adjacent post. Have your assistant pull the wire infill taut. Position a fencing staple so it crosses a welded or woven intersection diagonally. Attaching both vertical and horizontal wires to the post reduces shifting of the infill. Hammer the fencing staple into the post, securing the infill to the post. Staple the infill to the post at intersections not further than 6 inches apart.
Working toward the corner post, stretch and staple the wire infill to each fencepost. At the corner post, attach the infill at each intersection. Use the wire-cutting portion of the fencing pliers to trim excess infill material.
Trim broken wire infill material from the fence posts, using the wire-cutting portion of the fencing pliers. Leave functioning infill attached to the posts.
Unroll enough fencing material to extend between the posts where you removed the infill. Attach the free end of the fencing material to one post, using fencing staples.
Instruct an assistant to grasp the free end of the new fencing material with a fence stretcher just past the adjacent post and to pull the material taut. Staple the new infill material to the second post. Use the wire-cutting portion of the fencing pliers to trim excess infill material from both posts.