Relation extraction is a crucial language processing task for various downstream applications, including knowledge base completion, question answering, and summarization. Traditional relation-extraction techniques, however, rely on a predefined set of relations and model the extraction as a classification task. Consequently, such closed-world extraction methods are insufficient for inducing novel relations from a corpus. Unsupervised techniques like OpenIE, which extract <head, relation, tail> triples, generate relations that are too general for practical information extraction applications. In this work, we contribute the following: 1) We motivate and introduce a new task, corpus-based task-specific relation discovery. 2) We adapt existing data sources to create Wiki-Art, a novel dataset for task-specific relation discovery. 3) We develop a novel framework for relation discovery using zero-shot entity linking, prompting, and type-specific clustering. Our approach effectively connects unstructured text spans to their shared underlying relations, bridging the data-representation gap and significantly outperforming baselines on both quantitative and qualitative metrics. Our code and data are available in our GitHub repository.