Answer for USA, Canada and countries running a 60 Hertz supply service.
Dryer plug three to four
Yes this is possible and for safety's sake highly recommended. Instructions should come with the new cord. Open up the electrical access panel on the back of the dryer. You will see a terminal block with three wires going into it from the plug cord assembly. A red and black and white are now connected to the terminal strip. Look at the position and colours of the existing 3 prong cord and how it is connected. Make a diagram. Coloured wires on the outside terminals white in the center. From the center wire terminal you will see a jumper strap that goes to the frame of the dryer. When installing the four prong plug this jumper is removed completely. The kit should have with it a grounding lug that connects to where the removed grounding strip attached to the frame of the dryer. This is the attachment point for the fourth green ground wire from the new dryer cord assembly.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized
IF YOU ARE NOT REALLY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.