When moving an electric dryer or range to a new (to it) dwelling, it is not unusual to have to replace the "cord" (pigtail) on the appliance. Look carefully at the outlet in the house and go to a hardware store, appliance store, or electrical supply store for a matching pigtail. These tend to run $20–30 at big box retailers and a little more at electrical suppliers.
If the outlet is unusual, it might be more expedient to replace it instead of tracking down a hard-to-find pigtail. Many do-it-yourselfers are uncomfortable working on 240 volt and/or high power outlets, so you might prefer to hire an electrician. However, since this is a DIY board, it isn't all that difficult once you understand the legal and electrical technicalities.
Old (pre-2000 or so) appliance outlets in North America used 3 wires: 2 hot wires and one neutral. Installations since then have added a 4th wire for ground. Your local code requirements may allow grandfathering existing three wire systems to remain in place for a simple outlet replacement. Other regions may require upgrading to 4 wire. Check out what your requirements are.
Replacing the outlet is fairly straightforward: shut off the circuit breaker. Check the outlet with a DMM or voltage tester to assure yourself it is really dead. Undo the retaining screws, pull out the outlet. This will require some strength due to the thick and stiff conductors, either 10, 8, or 6 gauge. Note carefully which wires are hot and which are neutral or ground. Unscrew the outlet's terminal screws and pull the wires out. If there is any discoloration or scorched insulation, trim the wire and re-strip.
Insert wires into the appropriate terminals on the new outlet and tighten securely. Ease the outlet back into the wall and screw into place. Turn on the breaker and check voltages are applied in the correct positions. Turn breaker off before inserting appliance pigtail and then back on once it is securely inserted.