Foreign tourism operators with operations in Iceland
The Icelandic Tourist Board, the Icelandic Transport Authority and the Directorate of Labor have published informational brochures for foreign tourism operators with operations in Iceland:
Permit to operate in Iceland for passenger transport
Operators holding a valid permit from a country within the European Economic Area (EEA) may carry passengers for commercially in Iceland if they have a Community permit from their country of origin. This applies only to buses, cars for 9 or more passengers, and is according to European regulation EC nr. 1073/2009
Operators engaged in commercial passenger transportation using vehicles that are for 8 or less passengers must apply for an operating permit from the Icelandic Transport Authority according to Icelandic laws and submit appropriate documents from their home country. The documents must be submitted in English and must be translated by a certified translator if originally in another language. See further conditions for an operating permit.
There are two types of permits for cars registered for 8 or less passengers:
Permits related to travel services: Cars registered for 8 or less passengers, intended for trips of at least half a day and a safety plan must be submitted to the Tourist Board
Permit for specially equipped cars: Cars registered for 8 or less passengers and as off-road vehicles (and have a tire size of at least 780 mm diameter)
One of the conditions of the operating permit is that the legal domicile of the operator is registered within the EEA and therefore parties outside the EEA cannot be issued such a permit in Iceland. Those who cannot obtain a passenger transport operator’s permit for this reason may hire an operator holding a valid permit to carry out the transport.
The driver must have the appropriate driving license at all times, to be able to drive with a passenger for business purposes or with a code 95 in a driving license.
If an applicant intends to use rental cars, they must have a valid inspection and registered in appropriate usage category.
You can read more about passenger transport permits here.

Service provider
The Icelandic Transport Authority