With the exception of EU/EEA citizens, all foreigners working in Norway must have a residence permit that gives them the right to work in Norway. This also applies to remote work.
It is considered remote work when you work for a Norwegian or foreign employer off-site (e.g. from a hotel, a home or similar). This also applies if you are self-employed in Norway or abroad.
This implies that you cannot, for example, work for your employer in your home country while you are in Norway on a visit or holiday, regardless of whether you are on a visa-free stay or if you have a visitor visa.
You may only work remotely in Norway if you have a residence permit that gives you the right to do so. There is no specific residence permit for remote work in Norway. To work remotely during your stay, you must have a residence permit that entitles you to work remotely, such as: