You'll need to pull a 10/3 from the panel to your new dryer receptacle location
The old way of wiring dryers (NEMA 10-30 with the dryer's chassis grounded using the neutral) was a terrible kludge, and rather unsafe at that since a fault in the dryer circuit neutral will render the dryer's chassis live, right next to the most-likely-grounded washing machine.
Since you're putting in a new receptacle in a new location, you'll need to do it right and pull a 10/3 W/G cable from the breaker box to the new dryer location -- neutral to neutral bar, ground to ground bar or combination bar if they are combined in a main panel, and the two hots to the existing 30A breaker, with the breaker turned off for all this of course. At the new receptacle location, a NEMA 14-30R will need to be fitted -- black and red to hots, white to neutral, and green or bare to ground.
Don't forget to change the dryer over to a 4-wire (NEMA 14-30P) cord and pull the dryer's bonding jumper while you're at it! You'll also need to use a torque screwdriver to tighten the breaker and panel lugs to the manufacturer-specified torque value (printed on the labeling for the breaker and panel) -- this is required by 2017 NEC 110.14(D).