Do you have a permanent residence permit or settlement permit?  
In that case, simply order a residence card.

British citizens moving to Norway after 1 January 2021 need to apply for a residence permit under the rules applying to citizens of non-EU/EEA countries.

In 2021, British citizens and their family members who had rights of residence in Norway by 31 December 2020 may, when entering Norway, present the EEA registration certificate issued by the police upon registration as proof of legal residence.

Family members who are not British citizens must bring the residence card they received from the police. If your registration certificate is unavailable to you, or you came to Norway before the registration arrangement was in place, you may bring a residence certificate issued by the Norwegian Tax Administration as proof that you reside in Norway.

You can order a residence certificate from the Tax Administration via Altinn. Please note that it takes a few days to receive, so please order your residence certificate in good time.

In addition to evidence of legal residence in Norway, you need to present a valid passport or travel document when checked on the border.