This paper studies the problem of novel category discovery on single- and multi-modal data with labels from different but relevant categories. We present a generic, end-to-end framework to jointly learn a reliable representation and assign clusters to unlabelled data. To avoid over-fitting the learnt embedding to labelled data, we take inspiration from self-supervised representation learning by noise-contrastive estimation and extend it to jointly handle labelled and unlabelled data. In particular, we propose using category discrimination on labelled data and cross-modal discrimination on multi-modal data to augment instance discrimination used in conventional contrastive learning approaches. We further employ Winner-Take-All (WTA) hashing algorithm on the shared representation space to generate pairwise pseudo labels for unlabelled data to better predict cluster assignments. We thoroughly evaluate our framework on large-scale multi-modal video benchmarks Kinetics-400 and VGG-Sound, and image benchmarks CIFAR10, CIFAR100 and ImageNet, obtaining state-of-the-art results.