I just renewed mine airport sticker. It was about 8:30 am and I was the first one there (opens at 8:00). I was in and out in 5 minutes. You need your permanent TNC license, drivers license, car registration and proof of insurance.
The permitting office is at the West end of Terminal A outside around the corner from the TNC/Taxi area. You can be dropped off and picked up when you are done or you can park in the terminal garage for $3. If you do it one day while you are driving you can simply drop off your rider and you will be in the airport queue during the process. When you are done you can go to the TNC lot and the timer will show where you stand but it will be lower than it was when you first got there since once you are in the queue you do not lose your place just because the circle is not showing. Just don't leave the queue area.