Greenland tectonic plate?

Greenland is not a distinct plate. Most of Greenland is identical to (and attached to) the nearby Canadian shield: same ages and same materials (going back to some of the oldest rocks ever found on earth so this core of the continent has been in existence for almost the entire history of the earth). Greenland has been (is) partially separated from Canada by an ancient rift system that formed on its west-south side, but ultimately, that rifting failed (stopped) and the main rift that is now the Atlantic Ocean continued northward along the east side of Greenland, causing Greenland to stay with North America and separate from Europe.

Greenland has been part of "North America" (more properly called Laurentia, perhaps) since the early Archaean and apparently has moved around as a more or less complete unit (Greenland and nearby northern Canada) for the past 3-4 billion years, with continental growth happening at the margins of that core.

Greenland used to be part of North America. About 140 million years ago, it started to split off, by Baffin Bay. Then about 69 million years ago, the southern part opened up, at Labrador Sea. But the splitting stopped and the rift closed about 30 million years ago. Since then, Greenland and North America have moved the same way.