Wooden stairs will inevitably start to wear down after years of use. Treads become squeaky and the bullnose edges become misshapen or dipped. It is not easy to remove one tread without having to dismantle half the staircase, so repairing a bullnose is not always recommended.
This is harder if your staircase is carpeted. Lift the carpet up to the stair you are working on. With the bullnose exposed use a jigsaw to remove the bullnose from the tread. Keep the blade in line with the riser of the step below. You should end up with a square-edged step.
Creating the new Bullnose
Take a piece of lumber the same thickness as the tread on the step. Use a router with a round over ‘bit’ measuring half the depth of the wood and run the router the full length along the edge of the lumber. This will create half a bullnose. Turn the lumber over and run the router along the bottom side. The router will cut a shape identical to the top part of the depth. You will then have created a bullnose. Cut the correct width from the lumber to match the outreach of an existing bullnose on a step above or below it.
Use epoxy wood glue and at least 6 thin wood screws to attach the new bullnose. Secure it tightly and replace the carpet after the glue has dried. This is by no means totally permanent but it will prevent having to replace the whole step.