Machine learning on heterogeneous graphs has experienced rapid advancement in recent years, driven by the inherently heterogeneous nature of real-world data. However, existing studies typically assume the graphs to be static, while real-world graphs are continuously expanding. This dynamic nature requires models to adapt to new data while preserving existing knowledge. To this end, this work addresses the challenge of continual learning on heterogeneous graphs by introducing the Meta-learning based Knowledge Distillation framework (MKD), designed to mitigate catastrophic forgetting in evolving heterogeneous graph structures. MKD combines rapid task adaptation through meta-learning on limited samples with knowledge distillation to achieve an optimal balance between incorporating new information and maintaining existing knowledge. To improve the efficiency and effectiveness of sample selection, MKD incorporates a novel sampling strategy that selects a small number of target-type nodes based on node diversity and maintains fixed-size buffers for other types. The strategy retrieves first-order neighbors along metapaths and selects important neighbors based on their structural relevance, enabling the sampled subgraphs to retain key topological and semantic information. In addition, MKD introduces a semantic-level distillation module that aligns the attention distributions over different metapaths between teacher and student models, encouraging semantic consistency beyond the logit level. Comprehensive evaluations across three benchmark datasets validate MKD's effectiveness in handling continual learning scenarios on expanding heterogeneous graphs.