Intent discovery in task-oriented dialogue is typically cast as single-turn intent classification, leaving systems brittle when user goals fall outside predefined inventories. We reformulate the task as multi-turn zero-shot intent discovery and present KSTC, a framework that (i) embeds dialogue contexts, (ii) performs coarse clustering, (iii) generates predicted theme label for each cluster, (iv) refines clusters using the Large Language Model (LLM) using predicted theme label, and (v) relocates utterances according to user’s preference. Because generating informative predicted theme label is crucial during the LLM-driven cluster refinement process, we propose the Task Independent Slots (TIS), which generates effective theme label by extracting verb and noun slot–value.Evaluated on DSTC12 Track2 dataset, KSTC took the first place, improving clustering and labeling quality without in-domain supervision. Results show that leveraging conversational context and slot-guided LLM labeling yields domain-agnostic theme clusters that remain consistent under distributional shift. KSTC thus offers a scalable, label-free solution for real-world dialogue systems that must continuously surface novel user intents. We will release our code and prompts publicly.