PostNord AB is a private company and has been for some years, so the idea that this is a government service being withdrawn is untrue.
Danish law requires everyone to have access to postal services for letters. Therefore another private company, DAO, will provide postal delivery to everyone in Denmark and the ability for everyone in Denmark to send letters from DAO service points (in shops, etc).
A significant subsidy is being provided to DAO to enable a universal delivery service.
DAO will be the national postal service for international treaty (UPU) purposes, enabling letter and small parcel post between Denmark and other countries according to UPU agreements.