Yes, Greenland has been an autonomous territory within the Kingdom of Denmark since 1979, and it has its own government and institutions, including a Prime Minister. In fact, prior to gaining independence from Denmark through a self-determination process in 2020, Greenland had already developed a significant degree of autonomy.

The article you linked mentions that Donald Trump once made headlines by saying he thought Greenland would be a good place to buy, with him tweeting "Denmark, essentially." However, I couldn't find any information about Greenland gaining independence from Denmark. Instead, in June 2021, the Danish parliament voted to grant Greenland greater autonomy, but it remains part of the Kingdom of Denmark.

Greenland has a population of around 56,000 people and a relatively developed economy, driven by fishing, tourism, and oil extraction.