Classical knowledge graph completion (KGC) methods rely solely on structural information, struggling with the inherent sparsity of knowledge graphs (KGs). Large Language Models (LLMs) learn extensive knowledge from large corpora with powerful context modeling, which is ideal for mitigating the limitations of previous methods. Directly fine-tuning LLMs offers great capability but comes at the cost of huge time and memory consumption, while utilizing frozen LLMs yields suboptimal results. In this work, we aim to leverage LLMs for KGC effectively and efficiently. We capture the context-aware hidden states of knowledge triples by employing prompts to stimulate the intermediate layers of LLMs. We then train a data-efficient classifier on these hidden states to harness the inherent capabilities of frozen LLMs in KGC. We also generate entity descriptions with subgraph sampling on KGs, reducing the ambiguity of triplets and enriching the knowledge representation. Extensive experiments on standard benchmarks showcase the efficiency and effectiveness of our approach. We outperform classical KGC methods on most datasets and match the performance of fine-tuned LLMs. Additionally, compared to fine-tuned LLMs, we boost GPU memory efficiency by \textbf{$188\times$} and speed up training+inference by \textbf{$13.48\times$}.