A hole saw, found at your local hardware store is the solution. Most come in simple kits with many hole saw diameters and fit into your portable or cordless drill. Perform the following steps:
Take a six-inch length of scrap 1in.X3in. or 1in.X4in. and drill a pilot hole in the center.
Clamp the scrap wood with pilot hole on the door, centered over the existing lock-set hole. Centering can be accomplished by measuring or by putting a dowel through the pilot hole and visually aligning the scrap.
Select the appropriate size hole saw per the new lock-set's instructions and mount in the drill.
Using the pilot hole as a guide, drill the new hole through the scrap wood and the door.
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