As sounds carry rich information, environmental sound classification (ESC) is crucial for numerous applications such as rare wild animals detection. However, our world constantly changes, asking ESC models to adapt to new sounds periodically. The major challenge here is catastrophic forgetting, where models lose the ability to recognize old sounds when learning new ones. Many methods address this using replay-based continual learning. This could be impractical in scenarios such as data privacy concerns. Exemplar-free methods are commonly used but can distort old features, leading to worse performance. To overcome such limitations, we propose an Acoustic Feature Transformation (AFT) technique that aligns the temporal features of old classes to the new space, including a selectively compressed feature space. AFT mitigates the forgetting of old knowledge without retaining past data. We conducted experiments on two datasets, showing consistent improvements over baseline models with accuracy gains of 3.7\% to 3.9\%.