A few specific parts of GDPR do most of the work when it comes to physical documents. A regulator asking about print will point at these first, so understanding what each one requires is the foundation of a solid compliance posture.
Article 32 (security of processing) requires the controller and processor to implement "appropriate technical and organisational measures to ensure a level of security appropriate to the risk," with specific attention to accidental loss, unauthorized disclosure, and unauthorized access to personal data. For print, that translates into practical controls: secure release so documents do not sit on shared trays, access restrictions on who can print what, and safeguards against unauthorized viewing of output.
Article 28 (processor obligations) applies to your print vendor. Under GDPR, a controller can only use processors that provide "sufficient guarantees" of appropriate technical and organizational measures, and any subprocessors those vendors use are held to the same standard. In practice, this means your print vendor is a data processor, and you should have a signed data processing agreement in place that covers how personal data is handled, stored, and passed downstream. Most organizations do not have one, and most print vendors do not offer one by default.
Article 30 (records of processing) requires the controller to maintain records of processing activities and make them available to supervisory authorities on request. Printed output is a category of processing, which means an organization has to be able to demonstrate what was printed, by whom, and under what lawful basis. This is the accountability gap most organizations cannot close today, because the systems that would produce those records were never designed with regulatory reporting in mind.
The obligations are specific, but meeting them relies on the same kind of visibility, control, and documentation that already governs other parts of the data protection program.