As per the current norms, for entry into Iceland all travellers need to pre-register at covid.is, carry certificate of full vaccination (14 days must have elapsed since the second dose of vaccine for a certificate to be valid) or a certificate of previous infection and must present a negative RTPCR test report taken 72 hrs before departure on the first leg of the trip. If any of the necessary requirements are missing, the passenger must undergo double testing with a 5 day quarantine in between tests.
As the country wise entry requirements for travel are dynamic and change frequently all over the world, it is always advisable to be fully aware of all prevailing COVID related norms before travelling to any country.