On the other hand, if your paper certificate was issued under FAR 61.75 on the basis of a UK licence which will now have changed to an EASA licence you can still use the special process for reissuance described here:
https://www.faa.gov/licenses_certifi...fication/easa/
This involves a visit to Gatwick as described here:
Re-issue of FAA Certificate for UK licences issued after 17 September 2012 | Private Pilots | Personal Licences and Training