An increasingly massive number of remote-sensing images spurs the development of extensible object detectors that can detect objects beyond training categories without costly collecting new labeled data. In this paper, we aim to develop open-vocabulary object detection (OVD) technique in aerial images that scales up object vocabulary size beyond training data. The performance of OVD greatly relies on the quality of class-agnostic region proposals and pseudo-labetls for novel object categories. To simultaneously generate high-quality proposals and pseudo-labels, we propose CastDet, a CLIP-activated student-teacher open-vocabulary object Detection framework. Our end-to-end framework following the student-teacher self-learning mechanism employs the RemoteCLIP model as an extra omniscient teacher with rich knowledge. By doing so, our approach boosts not only novel object proposals but also classification. Furthermore, we devise a dynamic label queue strategy to maintain high-quality pseudo labels during batch training. We conduct extensive experiments on multiple existing aerial object detection datasets, which are set up for the OVD task. Experimental results demonstrate our CastDet achieving superior open-vocabulary detection performance, e.g., reaching 46.5% mAP on VisDroneZSD novel categories, which outperforms the state-of-the-art open-vocabulary detectors by 21.0% mAP. To our best knowledge, this is the first work to apply and develop the open-vocabulary object detection technique for aerial images. The code is available at https://github.com/lizzy8587/CastDet.