I have a 2018 Discovery XLE.  LOVE IT.

My water pump has started stuttering when using it, runs, stops, runs stops... 

We are fine on city water but pump will not maintain pressure.. Any ideas?

Also when looking just in case we need to replace it, we cannot find the existing model 4008-101-f65.

Could there be air in the lines? There are filters by the pump. One is about the size of your thumb. See if you get just water and no air.