The Government of Iceland has announced that it expects to start easing restrictions on international arrivals no later than 15 June 2020, while from 15 May, some professionals arriving in Iceland including scientists, filmmakers and athletes will be eligible for a modified quarantine. So, no need for exemptions after June 15th.
No later than 15 June 2020, travellers are expected to be given a choice between a two-week quarantine or being tested for the virus upon arrival, or otherwise proving that they are free of coronavirus infection. Exact requirements are still being developed but travellers will likely be required to download and use the official tracing app already in use. The app stores all location data locally on the user’s device and is only released for tracing purposes in case of an infection.