New Intent Discovery (NID) aims to recognize known and infer new intent categories with the help of limited labeled and large-scale unlabeled data. The task is addressed as a feature-clustering problem and recent studies augment instance representation. However, existing methods fail to capture cluster-friendly representations, since they show less capability to effectively control and coordinate within-cluster and between-cluster distances. Tailored to the NID problem, we propose a Robust and Adaptive Prototypical learning (RAP) framework for globally distinct decision boundaries for both known and new intent categories. Specifically, a robust prototypical attracting learning (RPAL) method is designed to compel instances to gravitate toward their corresponding prototype, achieving greater within-cluster compactness. To attain larger between-cluster separation, another adaptive prototypical dispersing learning (APDL) method is devised to maximize the between-cluster distance from the prototype-to-prototype perspective. Experimental results evaluated on three challenging benchmarks (CLINC, BANKING, and StackOverflow) of our method with better cluster-friendly representation demonstrate that RAP brings in substantial improvements over the current state-of-the-art methods (even large language model) by a large margin (average 5.5% improvement).