Greenland was an island and part of the Kingdom of Denmark. In 1002, the First Doctor, Susan Foreman, Ian Chesterton and Barbara Wright visited Greenland and met Eric the Red, who discovered Greenland, convincing him to take them to Newfoundland to obtain the plutonic ore the Doctor needed to refuel the TARDIS' batteries. (COMIC: Who Discovered America?)
Upon helping the Twelfth Doctor release a creature from the bottom of the River Thames, Bill Potts feared that they had doomed Greenland. (TV: Thin Ice)