Permanent Residence Permit
You can apply for a permanent residency permit if you have lived in Iceland for four years on a temporary residency permit that creates the eligibility for permanent residency.
The following temporary residence permits create eligibility to apply for a permanent residence permit:
work requiring expert knowledge
shortage of workers
family reunification (for spouses, cohabitating partners, children, parents, etc.)
special ties to the country
student (with limitations)