Yes, they do! White-tailed eagles, also called sea eagles, are the species of eagle that call Iceland home. They are a rather rare species here, with only 85 adult nesting pairs in all of Iceland. They were actually quite endangered in the middle of last century, with only around 20 breeding pairs, but they have since rebounded with conservation efforts and are protected.
As their name suggests, they like to be close to the sea, where they can fish. They are excellent fishers, but are also happy to scavenge.
They require either forests or cliffs for nesting, so given the lack of established forests in Iceland, they make their homes on sea cliffs and other inaccessible areas. Ornithologists actually think that they originally preferred to nest in the lowlands, but that they were pushed to nest in mountains and cliffs because of human hostility. They can also sometimes be seen on skerries and other islets.
One of their biggest habitats is in Breiðafjörður, where a majority of the nesting population lives.
Of course, we hope it goes without saying that you should not get too close to any sea cliffs when looking for eagles, and to treat them with respect and distance!