You can freely hike anywhere in greenland as there is no property ownership anywhere in the country. do go off the few small walking paths that exist. you will easily find yourself in offbeat locales, and wonder if you are perhaps the first person to ever stand in that particular spot. this rare sensation is by far the best reason to travel in greenland.
Skilled workers K-12 teachers and doctors in particular are always needed, knowledge of Danish or Greenlandic preferably both are necessary, although the University of Greenland in Nuuk does offer some programs in English. Foreigners, including most EU/EEA nationals Greenland is not part of the EU/EEA require a work permit in advance, which needs to be vetted and approved both by the Danish immigration authorities and the Government of Greenland. Danish citizens and other nationals of the Nordic Passport Area Norway, Sweden, Finland, and Iceland are exempt. Certain types of short-term work teaching, performing, installation technicians, construction, among others for less than 90 days does not require a work permit, nor does short-term research. See
If you have residency permanent or temporary in Denmark, you do not have any automatic immigration privileges in Greenland, although you can visit for up to 90 days without a visa even if you are a citizen of a country that would normally require one. Keep in mind that under Danish immigration law, time spent in Greenland is considered time outside of Denmark for residence permit purposes, and a long visit or work assignment in Greenland eg 6 months or more could cause your permit to lapse. Contact the immigration department if this may apply to you. Note that for purposes of applying for Danish citizenship, time spent in Greenland fully counts as it is part of the Kingdom of Denmark.