Fish Feeding Intensity Assessment (FFIA) is crucial in industrial aquaculture management. Recent multi-modal approaches have shown promise in improving FFIA robustness and efficiency. However, these methods face significant challenges when adapting to new fish species or environments due to catastrophic forgetting and the lack of suitable datasets. To address these limitations, we first introduce AV-CIL-FFIA, a new dataset comprising 81,932 labelled audio-visual clips capturing feeding intensities across six different fish species in real aquaculture environments. Then, we pioneer audio-visual class incremental learning (CIL) for FFIA and demonstrate through benchmarking on AV-CIL-FFIA that it significantly outperforms single-modality methods. Existing CIL methods rely heavily on historical data. Exemplar-based approaches store raw samples, creating storage challenges, while exemplar-free methods avoid data storage but struggle to distinguish subtle feeding intensity variations across different fish species. To overcome these limitations, we introduce HAIL-FFIA, a novel audio-visual class-incremental learning framework that bridges this gap with a prototype-based approach that achieves exemplar-free efficiency while preserving essential knowledge through compact feature representations. Specifically, HAIL-FFIA employs hierarchical representation learning with a dual-path knowledge preservation mechanism that separates general intensity knowledge from fish-specific characteristics. Additionally, it features a dynamic modality balancing system that adaptively adjusts the importance of audio versus visual information based on feeding behaviour stages. Experimental results show that HAIL-FFIA is superior to SOTA methods on AV-CIL-FFIA, achieving higher accuracy with lower storage needs while effectively mitigating catastrophic forgetting in incremental fish species learning.