The field of open relation extraction (ORE) has recently observed significant advancement thanks to the growing capability of large language models (LLMs). Nevertheless, challenges persist when ORE is performed on specific topics. Existing methods give sub-optimal results in five dimensions: factualness, topic relevance, informativeness, coverage, and uniformity. To improve topic-oriented ORE, we propose a zero-shot approach called PriORE: Open Relation Extraction with a Priori seed generation. PriORE leverages the built-in knowledge of LLMs to maintain a dynamic seed relation dictionary for the topic. The dictionary is initialized by seed relations generated from topic-relevant entity types and expanded during contextualized ORE. PriORE then reduces the randomness in generative ORE by converting it to a more robust relation classification task. Experiments show the approach empowers better topic-oriented control over the generated relations and thus improves ORE performance along the five dimensions, especially on specialized and narrow topics.