Clinical algorithms increasingly influence medication surveillance, alert prioritization, risk estimation, prescription review, and other pharmacy-related decisions. Yet institutions commonly govern their acquisition, technical installation, clinical validation, and day-to-day use through separate processes that do not establish a coherent decision about whether an algorithm should be allowed to enter, remain within, or leave medication-use practice. This article proposes a Pharmacy Algorithm Gatekeeping Architecture that treats algorithmic admission as a continuing institutional governance decision rather than a one-time technical approval. The architecture comprises a Pharmacy Algorithm Dossier, multidisciplinary gatekeeping review, bounded Permission Envelope, monitored-use layer, documented state transitions, and re-entry review. Admission is conditioned on the algorithm’s intended task, users, population, setting, data dependencies, permitted outputs, degree of autonomy, uncertainty handling, safety controls, equity implications, and monitoring readiness. Continuing permission may be narrowed through restriction, interrupted through suspension, or revoked through withdrawal when evidence, performance, workflow, safety, accountability, or implementation conditions become unacceptable. Remediation does not automatically restore permission; re-entry requires a renewed assessment capable of producing different boundaries or rejection. Evaluation must extend beyond model accuracy to calibration, human–AI joint performance, medication-safety consequences, workflow effects, subgroup performance, implementation fidelity, incident detection, and governance traceability. The architecture is an original non-empirical synthesis whose components and transition rules require prospective, comparative, and setting-specific validation. It does not replace regulatory authorization, professional judgment, local legal duties, or clinical accountability, and it does not establish that any admitted algorithm is universally safe, effective, or ready for unrestricted use.