Customer's initial NFIP flood policy effective in Nov. 2017 included a grandfathering provision, lists flood zone rated as X and current zone of AE. Customer changed flood insurance providers in 2019, using a third party provider and flood policy now lists a flood risk zone of X and flood rated zone of X. "Current zone" is not included on the policy and under "Grandfathered" it states N. Can a zone be carried over from an NFIP policy to a third party policy under the "grandfathering rule" or how does this work?

What is a third party policy? You mean a write-your-own insurance agent? Those are still NFIP policies.

It is now a private policy.

Zones do not matter on a private policy. You have to compare the private policy with the mandatory acceptance requirements - it say nothing about zones - that is a NFIP rating system only.