The emergence of quantum computing poses a significant threat to the cryptographic foundations that secure modern cloud infrastructures. Existing deployments of Zero Trust Architecture (ZTA) are largely built on classical cryptographic techniques such as the RSA algorithm and elliptic curve cryptography, which are vulnerable to future quantum attacks. Moreover, current studies offer limited guidance on how PQC can be integrated into cloud-native Zero Trust environments while guaranteeing operational efficiency and addressing adaptive security needs. The present study introduces an Adaptive Post Quantum Zero Trust (Adaptive PQC-ZT) Framework by combining the NIST recommended post quantum cryptographic algorithms with a policy based Crypto-Agility Engine for algorithm dynamic selection based upon Security Sensitivity, Algorithm Characteristics, and Latency. The framework was evaluated using publicly available PQC benchmark dataset containing 37,004 key encapsulation mechanism (KEM) records and 71,456 digital signature records. The analysis examined latency, communication overhead, security levels, and workload suitability for ML-KEM and ML-DSA algorithm families across representative cloud deployment scenarios. The results demonstrate that ML-KEM algorithms provide quantum-resistant key establishment with sub-millisecond latency, while ML-DSA algorithms significantly outperform SPHINCS+ variants in execution efficiency and communication overhead. The proposed Crypto-Agility Engine helps match cryptographic configuration with the needs of different workloads.