Are processor contracts a new legal requirement under GDPR?

Yes

The GDPR makes written contracts between controllers and processors a general requirement, rather than just a way of demonstrating compliance with the seventh data protection principle (appropriate security measures) under the DPA.

These contracts must now include certain specific terms, as a minimum.

These terms are designed to ensure that processing carried out by a processor meets all the requirements of the GDPR (not just those related to keeping personal data secure).