Recently, several researchers motivated the need to integrate Zero Trust (ZT) principles when designing and implementing authentication and authorization systems for IoT. An integrated Zero Trust IoT system comprises the network infrastructure (physical and virtual) and operational policies in place for IoT as a product of a ZT architecture plan. This paper proposes a novel Zero Trust architecture for IoT systems called ZTA-IoT. Additionally, based on different types of interactions between various layers and components in this architecture, we present ZTA-IoT-ACF, an access control framework that recognizes different interactions that need to be controlled in IoT systems. Within this framework, the paper then refines its focus to object-level interactions, i.e., interactions where the target resource is a device (equivalently a thing) or an information file generated or stored by a device. Building on the recently proposed Zero Trust score-based authorization framework (ZT-SAF) we develop the object-level Zero Trust score-based authorization framework for IoT systems, denoted as ZTA-IoT-OL-SAF, to govern access requests in this context. With this machinery in place, we finally develop a novel usage control model for users-to-objects and devices-to-objects interactions, denoted as UCON IoT . We give formal definitions, illustrative use cases, and a proof-of-concept implementation of UCON IoT . This paper is a first step toward establishing a rigorous formally-defined score-based access control framework for Zero Trust IoT systems.