<p>Zero Trust networks (ZTNs) enforce continuous authentication and least-privilege access, requiring strict policy compliance for each service request across dynamic, cross-domain, and heterogeneous environments. These policies depend on the ordered forwarding of Service Function Chains (SFCs) to reliably execute critical security functions such as authentication, inspection, and isolation. However, node failures, link fluctuations, and frequent policy updates can disrupt SFCs, undermining Zero Trust assurance. A key challenge is thus achieving highly reliable yet cost-efficient SFC orchestration under resource constraints. To address this, we propose a Backup and Reliable-aware VNF Submodular Optimization (BRVSO) mechanism that minimizes resource and operational costs while ensuring service reliability. The problem is decomposed into two coupled sub-tasks: primary chain mapping and backup deployment, each formulated as a monotone submodular optimization. By exploiting the diminishing returns property of submodular functions, we design two efficient algorithms: the Submodular Optimization-based Mapping Algorithm (SOMA) and the Submodular Optimization-based Backup Algorithm (SOBA), which collectively enable effective service path and backup resource allocation. Theoretical analysis confirms strong approximation guarantees. Experimental evaluations across multiple representative scenarios demonstrate that our approach significantly improves SFC acceptance rates while reducing resource overhead compared to existing baselines.</p>