Install new wall outlet few feet to the left of existing outlet
You can carefully remove the cove at the bottom of the wall. Then cut the drywall out from the area behind the base cove. You will need to notch the plate back so you can fish the NM behind the dry wall. Run the NM to the new location and repeat the notching up toward the new hole you just cut to install the cut-in box. Connect up the new receptacle put on the cover plate, then make up the connection at the old receptacle location (make sure the circuit is turned off). Replace the base turn on the power and you're good to go.

Stay safe and good luck.