Continual Knowledge Graph Embedding (CKGE) aims to continually learn embeddings for new knowledge, i.e., entities and relations, while retaining previously acquired knowledge. Most existing CKGE methods mitigate catastrophic forgetting via regularization or replaying old knowledge. They conflate new and old knowledge of an entity within the same embedding space to seek a balance between them. However, entities inherently exhibit multi-faceted semantics that evolve dynamically as their relational contexts change over time. A shared embedding fails to capture and distinguish these temporal semantic variations, degrading lifelong link prediction accuracy across snapshots. To address this, we propose a Multi-Faceted CKGE framework (MF-CKGE) for semantic-aware link prediction. During offline learning, MF-CKGE separates temporal old and new knowledge into distinct embedding spaces to prevent knowledge entanglement and employs semantic decoupling to reduce semantic redundancy, thereby improving space efficiency. During online inference, MF-CKGE adaptively identifies semantically query-relevant entity embeddings by quantifying their semantic importance, reducing interference from query-irrelevant noise. Experiments on eight datasets show that MF-CKGE achieves an average (maximum) improvement of 1.7% (2.7%) and 1.4% (3.8%) in MRR and Hits@10, respectively, over the best baseline. Our source code and datasets are available at: https://anonymous.4open.science/r/MF-CKGE-04E5.