

It’s not shown on the list of NATO members because it’s not a separate country. Other islands like Bornholm and Zealand are obviously also not shown, because they are Denmark. So is Greenland. They are not independent, though both Denmark and Greenland has worked towards that in many years.
Greenland was part of NATO since the beginning, and you could even argue that it was before that, because the collaboration between Denmark and USA on military control of Greenland predates NATO.
Because Denmark is a democracy and the people on Greenland has voted towards independence. Denmark is not keeping them from seceding, but their economy has kept them from doing it before.
An independence referendum has not been done yet, but once they do it, Denmark will most likely accept the outcome without objections. Iceland did the same thing in 1918.
https://en.wikipedia.org/wiki/Greenlandic_independence