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Authentication, authorization, and trust verification are central parts of an access control system. The conditions for granting access in such a system are collected in access policies. Since access conditions are often complex, dedicated languages -- policy languages -- for defining policies are in use. However, current policy languages are unable to express such conditions having privacy of users in mind. With privacy-preserving technologies, users are enabled to prove information to the access system without revealing it. In this work, we present a generic design for supporting privacy-preserving technologies in policy languages. Our design prevents unnecessary disclosure of sensitive information while still allowing the formulation of expressive rules for access control. For that we make use of zero-knowledge proofs (NIZKs). We demonstrate our design by applying it to the TPL policy language, while using SNARKs. Also, we evaluate the resulting ZK-TPL language and its associated toolchain. Our evaluation shows that for regular-sized credentials communication and verification overhead is negligible.