New Pressure Tank-Cloudy Water

We replaced our ancient pressure tank today and the water is now cloudy. Do I need to run the water to clear it up or just let it settle?

I'd try to run it out from an outside spigot. If you do it inside, remove the aerator to get more flow and so it doesn't clog up.

Valveman described it best

You may have to pull the pump up and plug the valve (or hole in the drop pipe) as it lets air to enter the system. You may also need to cap or plug the Schrader valve on the check valve near the tank.

Should make sure it's entrained air by letting water stand in a clear glass overnight. Clear water, no sand in the bottom means entrained air most likely.