Abstract: Trajectory-based confidence estimation has shown promising performance for large language models (LLMs) by leveraging rich signals from their reasoning processes. However, we find that such confidence estimators can degrade substantially after agentic reinforcement learning (Agentic RL) as it induces substantial shifts in the reasoning trajectories. More importantly, despite these shifts, we uncover a reliability structure that is largely preserved across Base and RL models: $\textbf{more}$ $\textbf{stable}$ $\textbf{trajectories}$ $\textbf{remain}$ $\textbf{more}$ $\textbf{likely}$ $\textbf{to}$ $\textbf{produce}$ $\textbf{correct}$ $\textbf{answers}$. This preserved relationship provides a transferable, label-free reliability signal for post-RL confidence adaptation. Building on this finding, we propose $\textbf{StaR-TTA}$, a stability-guided framework for label-free test-time confidence adaptation. StaR-TTA jointly learns from correctness supervision and stability-derived reliability supervision on labeled Base trajectories, establishing the connection between trajectory stability and answer reliability. At test time, it reuses stability-induced reliability rankings from unlabeled RL trajectories to adapt confidence scores to the shifted trajectory distribution, without requiring target correctness labels. Across four QA benchmarks, StaR-TTA achieves an average AUROC of \(0.721\), with consistent improvements across unseen datasets, model families and scales, and different Agentic RL algorithms.