<p>Predictive Process Monitoring (PPM) aims to forecast the future behavior of an ongoing process instance based on historical event logs. PPM approaches which follow an offline training and online prediction paradigm, often struggle to adapt to the evolving nature of real-world processes. While state-of-the-art approaches address such challenges by continuously updating or retraining models, they typically overlook dynamic processes, where numerous unseen activities emerge or the order between activities evolves over time. To address this gap, we propose the Drift-Adaptive Class Incremental Learning (DA-CIL) framework for next activity prediction in dynamic process environments. DA-CIL employs a representation-based drift detection mechanism to identify shifted or unseen activities. To enhance model generalization to drifting patterns, DA-CIL applies data augmentation in feature space to generate diverse and novel feature representations that are unseen but likely to occur as processes evolve. Upon drift detection, the model is incrementally updated to the newly observed data in combination with augmented samples and knowledge distillation. Experiments on real-life event logs demonstrate that DA-CIL consistently outperforms existing methods in prediction accuracy and adaptation efficiency, highlighting its effectiveness for next activity prediction in highly dynamic process environments.</p>