Yes, it is possible to work in Iceland. EFTA (European Free Trade Association) and EEA (European Economic Area) country members can live and work for three months. After that, they need visas or working permits and residential registration at the country's national registry.
As a country that welcomes around 2 million tourists per year (six times its population), there are many job opportunities in the tourism industry in Iceland. Sectors like construction, healthcare, and IT are continuously hiring too. Other pillar industry branches include aluminum smelting, fish processing, geothermal, and hydropower.