Generalized Category Discovery (GCD) aims to recognize unlabeled images from known and novel classes by distinguishing novel classes from known ones, while also transferring knowledge from another set of labeled images with known classes. Existing GCD methods rely on self-supervised vision transformers such as DINO for representation learning. However, focusing solely on the global representation of the DINO CLS token introduces an inherent trade-off between discriminability and generalization. In this paper, we introduce an adaptive part discovery and learning method, called APL, which generates consistent object parts and their correspondences across different similar images using a set of shared learnable part queries and DINO part priors, without requiring any additional annotations. More importantly, we propose a novel all-min contrastive loss to learn discriminative yet generalizable part representation, which adaptively highlights discriminative object parts to distinguish similar categories for enhanced discriminability while simultaneously sharing other parts to facilitate knowledge transfer for improved generalization. Our APL can easily be incorporated into different GCD frameworks by replacing their CLS token feature with our part representations, showing significant enhancements on fine-grained datasets.