Extreme Multi-label Learning (XML) involves assigning the subset of most relevant labels to a data point from millions of label choices. A hitherto unaddressed challenge in XML is that of predicting unseen labels with no training points. These form a significant fraction of total labels and contain fresh and personalized information desired by end users. Most existing extreme classifiers are not equipped for zero-shot label prediction and hence fail to leverage unseen labels. As a remedy, this paper proposes a novel approach called ZestXML for the task of Generalized Zero-shot XML (GZXML) where relevant labels have to be chosen from all available seen and unseen labels. ZestXML learns to project a data point's features close to the features of its relevant labels through a highly sparsified linear transform. This L0-constrained linear map between the two high-dimensional feature vectors is tractably recovered through a novel optimizer based on Hard Thresholding. By effectively leveraging the sparsities in features, labels and the learnt model, ZestXML achieves higher accuracy and smaller model size than existing XML approaches while also promoting efficient training & prediction, real-time label update as well as explainable prediction.