Continual Knowledge Graph Embedding (CKGE) aims to efficiently learn new knowledge and simultaneously preserve old knowledge. Dominant approaches primarily focus on alleviating catastrophic forgetting of old knowledge but neglect efficient learning for the emergence of new knowledge. However, in real-world scenarios, knowledge graphs (KGs) are continuously growing, which brings a significant challenge to fine-tuning KGE models efficiently. To address this issue, we propose a fast CKGE framework (FastKGE), incorporating an incremental low-rank adapter (IncLoRA) mechanism to efficiently acquire new knowledge while preserving old knowledge. Specifically, to mitigate catastrophic forgetting, FastKGE isolates and allocates new knowledge to specific layers based on the fine-grained influence between old and new KGs. Subsequently, to accelerate fine-tuning, FastKGE devises an efficient IncLoRA mechanism, which embeds the specific layers into incremental low-rank adapters with fewer training parameters. Moreover, IncLoRA introduces adaptive rank allocation, which makes the LoRA aware of the importance of entities and adjusts its rank scale adaptively. We conduct experiments on four public datasets and two new datasets with a larger initial scale. Experimental results demonstrate that FastKGE can reduce training time by 34%-49% while still achieving competitive link prediction performance against state-of-the-art models on four public datasets (average MRR score of 21.0% vs. 21.1%). Meanwhile, on two newly constructed datasets, FastKGE saves 51%-68% training time and improves link prediction performance by 1.5%.