Abstract: Temporal knowledge graph (TKG) completion models typically rely on having access to the entire graph during training. However, in real-world scenarios, TKG data is often received incrementally as events unfold, leading to a dynamic non-stationary data distribution over time. While one could incorporate fine-tuning to existing methods to allow them to adapt to evolving TKG data, this can lead to forgetting previously learned patterns. Alternatively, retraining the model with the entire updated TKG can mitigate forgetting but is computationally burdensome. To address these challenges, we propose a general continual training framework that is applicable to any TKG completion method, and leverages two key ideas: (i) a temporal regularization that encourages repurposing of less important model parameters for learning new knowledge, and (ii) a clustering-based experience replay that reinforces the past knowledge by selectively preserving only a small portion of the past data. Our experimental results on widely used event-centric TKG datasets demonstrate the effectiveness of our proposed continual training framework in adapting to new events while reducing catastrophic forgetting. Further, we perform ablation studies to show the effectiveness of each component of our proposed framework. Finally, we investigate the relation between the memory dedicated to experience replay and the benefit gained from our clustering-based sampling strategy.