Active learning, which lets the model select the most informative data within a limited annotation budget for annotation, often achieves comparable performance with fewer labelled samples. However, despite its potential benefits, active learning has not been extensively explored in Named Entity Recognition (NER), as NER is considered more challenging than traditional tasks commonly addressed in the active learning literature. In this paper, we propose a novel deep active learning framework called Deep AUC Maximisation-based Active Learning (DAMAL), which learns uncertainty-aware representations for unlabeled data. Notably, DAMAL, due to its foundation in AUC maximisation, excels in addressing label sparsity, making it a well-suited approach for NER tasks. Experimental results across several NER tasks highlight the advantages of the proposed framework over existing active learning methods for NER.