Knowledge transfer between teacher and student models has proven effective across various machine learning applications. However, challenges arise when the teacher's predictions are noisy, or the data domain during student training shifts from the teacher's pretraining data. In such scenarios, blindly relying on the teacher's predictions can lead to suboptimal knowledge transfer. To address these challenges, we propose a novel and universal framework, Adaptive Uncertainty-guided Knowledge Transfer ($\textbf{AUKT}$), which leverages Conformal Prediction (CP) to dynamically adjust the student's reliance on the teacher's guidance based on the teacher's prediction uncertainty. CP is a distribution-free, model-agnostic approach that provides reliable prediction sets with statistical coverage guarantees and minimal computational overhead. This adaptive mechanism mitigates the risk of learning undesirable or incorrect knowledge. We validate the proposed framework across diverse applications, including image classification, imitation-guided reinforcement learning, and autonomous driving. Experimental results consistently demonstrate that our approach improves performance, robustness and transferability, offering a promising direction for enhanced knowledge transfer in real-world applications.