One way car hire Birmingham Airport and return Cheltenham

I can see you didn't make a search yet, the website will tell if it is possible. Follow the next instructions re. ONE WAY CAR HIRE:-

If you intend to drop off the vehicle in a different location from the pick up location, then tick the box “Return to a different location”. If then no cars are displayed at STEP2, then one way is not permitted between these locations.
For one way rentals sometimes it can be a fee. This is almost always included in the total rental rate and payable at the desk on arrival.

For drop off at a city location (Cheltenham) choose office ours and avoid Saturday afternoon and Sunday.

I can see you made a search now and don't see results (car photos). I had a look and it seems it is only possible to drop off the car in Gloucester. Reason might be that the location in Cheltenham is closed because of Covid.