Greenland is the world’s largest island when landmasses classified as continents are excluded.
Greenland covers about 2.17 million square kilometres, making it considerably larger than New Guinea, the second-largest island. Most of its surface is covered by the Greenland Ice Sheet, which is the second-largest ice body on Earth after Antarctica’s ice sheet.
Greenland is geographically part of North America. Politically, it is an autonomous territory within the Kingdom of Denmark, with extensive self-government introduced in 1979 and expanded in 2009. Nuuk is its capital and largest city.
Australia is larger than Greenland but is generally classified as a continent rather than an island, which explains the qualification in the question. Greenland’s ice sheet also makes maps misleading: the island’s apparent size on many world maps is exaggerated by projection, especially in Mercator-style maps.