3 prong to 4 prong dryer cord change
If you can remove the existing grounding wire from the grounding screw, then do that and connect your 4-prong's grounding wire to the screw. 

I initially misunderstood your explanation of the existing grounding wire. If this is a wire coming from inside the dryer, then you'll likely need to connect it to the neutral lug once you've connected to the grounding screw a suitable ground from your new 4 prong cable. As said in a comment, your best bet is to consult the dryer's manual to verify this is the correct action for this step.