Drill a hole through a 1-foot-long, 1-inch-by-4-inch board with a hole saw. This piece of board serves as the template for enlarging the hole in the door.
Center the template over the existing hole in the door and place the board without the hole over the door hole on the opposite side of the door. The solid board helps prevent splintering on the opposite side of the door when you drill the new hole.
Clamp the boards together over the door with two wood clamps. You must angle one of the clamps to clamp the ends of the boards nearest the center of the door. Ensure that the clamps do not cover the door hole.
Position the hole saw in the drill into the hole template. Squeeze the power trigger slowly to start drilling the new hole, allowing the template board to keep the hole saw straight.
Increase speed on the drill once the hole saw teeth begin cutting through the door. Keep drilling until the hole saw comes through the board on the opposite side. Remove the wood clamps and the two boards from the door.