There are new rules for travelling to Faroe Islands from 15th June 2020. Visitors from Denmark, Greenland, Iceland, Norway and Germany, can come to Faroe Islands, if they can provide proof of a negative COVID-19 test that has been taken within the last five days before departure.
If you are a resident in another country than stated above, you will not be able to travel to the Faroe Island without a recognised reason for coming to the Faroe Islands.
More info is available at corona.fo