Pre-trained language models have been widely exploited to learn dense representations of documents and queries for information retrieval. While previous efforts have primarily focused on improving effectiveness and user satisfaction, response time remains a critical bottleneck of conversational search systems. To address this, we exploit the topical locality inherent in conversational queries, i.e., the tendency of queries within a conversation to focus on related topics. By leveraging query embedding similarities, we dynamically restrict the search space to semantically relevant document clusters, reducing computational complexity without compromising retrieval quality. We evaluate our approach on the TREC CAsT 2019 and 2020 datasets using multiple embedding models and vector indexes, achieving improvements in processing speed of up to 10.4X with little loss in performance (4.4X without any loss). Our results show that the proposed system effectively handles complex, multiturn queries with high precision and efficiency, offering a practical solution for real-time conversational search.