Let's assume for a moment that the 3-prong plug is a 220v dryer plug and not a 120v receptacle.

If it is older wiring, it was probably done with 2 hots and a neutral/ground (3 wires). If so, you will need to pull new wiring with 2 hots, a neutral and a separate ground (4-wires) and connect it at both the panel and the new outlet.

The old way was two hots and a neutral. You were allowed to use the neutral for the equipment ground in this case. If you have such a grandfathered installation, you can put a three prong cord and plug on your new dryer. If you want a four prong receptacle, you will have to run new wiring as weedy says above.

Changing the 10 3 NMB ungrounded wiring from the circurit breaker to the ungrounded 10 3 outlet aka dedicated circurit. The original 240 volt 30 amp circurit breaker can be reused but new 10 4 NMB (black,red,white, bare ground wiring will need replaced from the original circurit breaker to the new 4 prong outlet. Also the old 10 3 dryer cord will need replaced with a new 10 4 dryer cord.

www,dbelectric.us