In recent years, there has been an increasing interest in claim detection as an important building block for misinformation detection. This involves detecting more fine-grained attributes relating to the claim, such as the claimer, claim topic, claim object pertaining to the topic, etc. Yet, a notable bottleneck of existing claim detection approaches is their portability to emerging events and low-resource training data settings. In this regard, we propose a fine-grained claim detection framework that leverages zero-shot Question Answering (QA) using directed questions to solve a diverse set of sub-tasks such as topic filtering, claim object detection, and claimer detection. We show that our approach significantly outperforms various zero-shot, few-shot and task-specific baselines on the NewsClaims benchmark (Reddy et al., 2021).