This paper proposes an autonomous trust orchestration method that performs task-specific trust assessments to ensure efficient task completion in distributed collaborative systems. To address the increasing complexity and resource consumption of the trust assessment process due to complex tasks, spatially and temporally dynamically distributed device resources, and inevitable assessment overhead, we leverage agent AI and a hypergraph based on the concept of a semantic chain-of-trust. Agent AI recognizes device status and autonomously performs trust assessments only during device idle time based on past performance data, enabling efficient utilization of distributed resources. Furthermore, task-specific trust assessments are performed by analyzing the alignment between resource capabilities and task requirements. A trust hypergraph containing trust semantics is maintained to manage collaborators hierarchically and identify those requiring trust assessments, thereby balancing overhead and trust accuracy. Multi-hop collaboration is supported by connecting local trust hypergraphs across multiple devices, enabling efficient coordination in large-scale systems. Experimental results demonstrate that the proposed method achieves resource-efficient trust assessments.