Present dryer receptacle is three prong with four wires; white wire is not connected. Changing to a 4 wire receptacle for a dryer.

There are plenty of sites that tell you how to do that.

The cord for the dryer needs to be changed. There is a green/white bonding jumper that needs to be removed in the dryer and green(gnd) and white(N) need to be connected.

Similarly at the plug.

Present dryer receptacle is three prong with four wires; white wire is not connected. Changing to a 4 wire receptacle for a dryer.If the white wire was not connected that was dangerous. It's a good thing you are replacing it.

The black and red are your two hots (gold screws). The white is the neutral (silver screw). Bare is the ground (green screw).