My registration renewal Is current on FAA.GOV but the new registration card has not arrived. I’ve applied for a replacement. May I fly until the replacement arrives?
No. 91.203(a)(2) clearly requires an effective registration paper "within" the aircraft. However, you can get them to fax a temporary certificate until the replacement arrives by snail mail. See https://www.faa.gov/licenses_certificates/aircraft_certification/aircraft_registry/replacement_aircraft_registration_certificate/.
This was very helpful, thanks. The only problem I encountered was that there was no response on the fax number or even at an alternative fax the examiner provided. But I was able to submit the required documentation via email. I was told to expect the temporary registration NLT tomorrow.