Autonomous agents in safety-critical applications must continuously adapt to dynamic conditions without compromising performance and reliability. Traditional approaches that rely on policy adaptation mechanisms have inherent limitations: symbolic approaches lack flexibility due to rigid structures, while reinforcement learning approaches incur costly retraining. The more recent approaches use end-to-end large language models (LLMs), which, despite enhanced adaptiveness, suffer from unacceptable inference latency and vulnerabilities, such as hallucinations that undermine real-time reliability. This work proposes $\textbf{TAPA}$ ($\textbf{T}$raining-free $\textbf{A}$daptation of $\textbf{P}$rogrammatic $\textbf{A}$gents), a framework that re-positions LLMs as intelligent action space moderators rather than direct decision-makers, enabling training-free action adaptation in evolving environments. TAPA decouples strategic intent from execution through logical primitive abstraction, allowing meta-agents to operate in an interpretable way over abstract, high-level actions. In the meantime, LLMs dynamically synthesize and adapt programs for the high-level actions, in order to respond promptly and correctly to environmental changes. In particular, our framework constructs program pools via a multi-scenario simulation with provenance chains, mitigating the scarcity of program samples in safety-critical domains, thereby facilitating program retrieval for familiar scenarios and generation for unseen situations. Extensive experiments across diverse complex domains validate TAPA's effectiveness, achieving optimal network uptime in cybersecurity and maintaining formation consensus in swarm intelligence tasks. This work promotes a paradigm shift for autonomous system design in evolving environments, from policy adaptation to dynamic action adaptation.