Autonomous AI agents are being deployed into consequential real-world workflows, yet the governance infrastructure supporting these deployments remains critically underdeveloped. Current approaches, such as static prompt-level constraints, post-incident redeployment cycles, and monitoring-only observability frameworks, share a common structural weakness: none of them makes governance intelligible to the agent itself. We introduce CARROTS'N'STICKS (Governance of autonomous agent behavior via dynamic privilege allocation and structured feedback injection), a runtime framework that treats the operational autonomy of an autonomous agent as a continuous function of its demonstrated behavioral compliance. CARROTS'N'STICKS continuously evaluates agent behavior against operator-defined policies, updates a recency-weighted trust score, and dynamically adjusts the agent's privilege state, the set of capabilities and access rights it is permitted to exercise, in response. Every privilege adjustment is accompanied by a structured feedback message injected directly into the agent's operational context, providing a causally-grounded, policy-cited learning signal upstream of the agent's next action decision. CARROTS'N'STICKS operates without stopping or restarting the governed agent, is framework-agnostic, and is applicable across language model-based agents, robotic systems, multi-agent networks, and hybrid human-AI workflows. This paper presents the motivation, conceptual architecture, distinguishing properties, and applicability of CARROTS'N'STICKS, situating it within the broader landscape of AI safety, agent governance, and enterprise deployment practice. Empirical validation across deployment contexts is reserved for future work. A provisional patent application covering the middleware described in this paper was filed with the USPTO on 31 May 2026.