The cost to hire an electrician to install a new electrical outlet will depend on if the electrician is just replacing the current outlet with a new electrical outlet or if the electrician is running a new wire to install a new electrical outlet where there was no electrical outlet previously.
If you just need an electrical outlet replaced it could cost $150.00 because of the service charge along with hourly rate to change out the outlet.
For an electrical outlet to be replaced it's best to look around for a handyman that would be cheaper.
To have a complete new outlet installed in a room where no outlet was before it can cost $250.00 to run the new electrical outlet because a new wire will need to be run along through your walls and/or ceiling and most electricians charge at least $100.00 for service charges and then $50.00 to $100.00 per hour for the labor plus the materials.
A few months ago I paid $250.00 to have a complete new electrical outlet installed in my bedroom which included running a new wire and installing a new breaker in the electrical panel.