Exception for public institution
According to the DPA, the conditions mentioned in Article 6 of the GDPR regarding legitimate interest do not apply to public institutions.
In Denmark, the age at which a child can provide a valid consent is reduced to 13 years old (DPA Section 6(3)). If the child is under 13, the processing is lawful only if and to the extent that the child’s responsible (DPA Section 6(3)).
The Data Protection Agency has published a guideline on consent (in Danish): https://www.datatilsynet.dk/media/6562/samtykke.pdf