I don't think it has to be an EASA reg. aircraft, and no requirement for a TRE either. A Class Rating Examiner should be sufficient.
However it has to be an approved EASA examiner. If your rating has not expired - I don't even see why the examiner would have to hold the local reg. license (for your EASA renewal), as long as it is on a certified (AFM) single pilot aero plane..