Machine learning on heterogeneous graphs has advanced rapidly, driven by the diverse entities, relations, and semantics inherent in real-world data. However, most existing studies assume static graphs, whereas real-world graph data are often continuously updated. Continual learning in this setting is particularly challenging because historical knowledge is encoded not only in target-node representations, but also in their heterogeneous structural contexts and relation-dependent semantic responses. To this end, we introduce HERO, a heterogeneous continual graph learning framework that preserves historical knowledge at both structural and semantic levels while adapting to incoming tasks. We analyze experience replay as an approximation to the unavailable historical gradient and decompose its error into target-selection and context-reconstruction terms. This analysis shows that replaying target nodes alone is generally insufficient for relation-sensitive HGNNs, as removing typed neighborhood context can alter both representations and historical gradients. Motivated by this, HERO employs DiSCo to select representative target nodes and reconstruct compact heterogeneous contexts through relation-aware multi-type neighbor expansion. To further preserve knowledge that cannot be captured by replayed subgraphs alone, HERO aligns task-conditioned predictions and heterogeneous semantic responses through multi-level knowledge distillation. A lightweight look-ahead adaptation step is additionally used to improve plasticity on incoming tasks. Experiments on four datasets with three HGNN backbones show that HERO achieves the best or tied-best average performance among state-of-the-art baselines, while maintaining competitive forgetting. Our code is available at https://github.com/gqBond/HCGL.

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