There's no issue of primacy between laws as GDPR explicitly states that processing of private data which is required by some local law is legitimate. GDPR does

There's no issue of primacy between laws as GDPR explicitly states that processing of private data which is required by some local law is legitimate. GDPR does apply to state and municipal institutions, requiring them to have a legal basis for processing private data, however, local laws can grant that legal basis and GDPR would not dispute it.