Does the NPR have any relation with NRC?

Yes, as per the preparation methodology prescribed in Citizenship (Registration of Citizen & Issue of NC) Rules 2003, it is from the NPR that data will be taken for Updation in the Local Register of Indian Citizen (i.e. part of NRC) after Scrutiny and Verification.

The government is yet to finalize the modalities of NPR-NRC and hence some pertinent and crucial questions like what is the cut-off date and what documents are valid for proving citizenship cannot be answered until rules are formulated to that regard.