Active learning is a commonly used approach that reduces the labeling effort required to train deep neural networks. However, the effectiveness of current active learning methods is limited by their closed-world assumptions, which assume that all data in the unlabeled pool comes from a set of predefined known classes. This assumption is often not valid in practical situations, as there may be unknown classes in the unlabeled data, leading to the active open-set annotation problem. The presence of unknown classes in the data can significantly impact the performance of existing active learning methods due to the uncertainty they introduce. To address this issue, we propose a novel data-centric active learning method called NEAT that actively annotates open-set data. NEAT is designed to label known classes data from a pool of both known and unknown classes unlabeled data. It utilizes the clusterability of labels to identify the known classes from the unlabeled pool and selects informative samples from those classes based on a consistency criterion that measures inconsistencies between model predictions and local feature distribution. Unlike the recently proposed learning-centric method for the same problem, NEAT is much more computationally efficient and is a data-centric active open-set annotation method. Our experiments demonstrate that NEAT achieves significantly better performance than state-of-the-art active learning methods for active open-set annotation.