Large Language Models (LLMs) suffer from a critical limitation: their knowledge is static and quickly becomes outdated. Retraining these massive models is computationally prohibitive, while existing knowledge editing techniques can be slow and may introduce unforeseen side effects. To address this, we propose DySK-Attn, a novel framework that enables LLMs to efficiently integrate real-time knowledge from a dynamic external source. Our approach synergizes an LLM with a dynamic Knowledge Graph (KG) that can be updated instantaneously. The core of our framework is a sparse knowledge attention mechanism, which allows the LLM to perform a coarse-to-fine grained search, efficiently identifying and focusing on a small, highly relevant subset of facts from the vast KG. This mechanism avoids the high computational cost of dense attention over the entire knowledge base and mitigates noise from irrelevant information. We demonstrate through extensive experiments on time-sensitive question-answering tasks that DySK-Attn significantly outperforms strong baselines, including standard Retrieval-Augmented Generation (RAG) and model editing techniques, in both factual accuracy for updated knowledge and computational efficiency. Our framework offers a scalable and effective solution for building LLMs that can stay current with the ever-changing world.