Do I need to remove the old wax before applying Liquid Wax

Yes, this needs to be the very first product applied to your vehicle. 

Clay bar would be best way to thoroughly remove any old wax/sealant. Using regular dish soap such as Dawn, mixed with water as your clay lube will also help to remove it. (also saves a lot of money instead of using regular clay lube) 

If you don't have the time or patience to clay bar your vehicle, dish soap and water should be sufficient to remove all your old wax/sealant.