According to the Danish Monarchy website:
In keeping with tradition, The Queen and The Prince Consort hold New Year’s levees at Amalienborg and Christiansborg Palace, respectively, at the beginning of the New Year.
For centuries, the Royal Danish House and Danes have wished each other a Happy New Year…. The origin of the contemporary New Year’s levees and New Year’s banquet is not known with certainty, but already in the mid 1600s the events around the changing of the year were referred to as old customs, and the basic elements are still the same.
To read the full post on the Danish Monarchy website, please click here.