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Low-carbon flexibility markets are becoming important tools for coordinating distributed energy resources, electric vehicles, storage, and responsive demand. Their practical value depends on how well they manage renewable forecast errors, uncertain prosumer behavior, and distribution-network constraints. This article develops a risk-aware optimization model for local flexibility market clearing under renewable forecast uncertainty, prosumer non-compliance, and feeder operating limits. The purpose is to reduce severe cost, carbon, and reliability outcomes rather than optimizing only average performance. The proposed model combines probabilistic renewable uncertainty, statistical prosumer compliance behavior, linearized distribution-network limits, and a conditional value-at-risk representation. The clearing problem is structured as a tractable optimization model suitable for commercial solvers. The model procures low-carbon flexibility while limiting exposure to delivery shortfalls and network infeasibility. The case study compares the proposed risk-aware clearing approach with deterministic and risk-neutral alternatives. The framework provides a practical risk-management tool for flexibility market operators. It supports reliable low-carbon dispatch while accounting for imperfect forecasts, incomplete prosumer delivery, and feeder constraints.