Structural Hole (SH) theory states that the node which acts as a connecting link among otherwise disconnected communities gets positional advantages in the network. These nodes are called Structural Hole Spanners (SHS). Numerous solutions are proposed to discover SHSs; however, most of the solutions are only applicable to static networks. Since real-world networks are dynamic networks; consequently, in this study, we aim to discover SHSs in dynamic networks. Discovering SHSs is an NP-hard problem, due to which, instead of discovering exact k SHSs, we adopt a greedy approach to discover Top-k SHSs. We first propose an efficient Tracking-SHS algorithm for updating SHSs in dynamic networks. Our algorithm reuses the information obtained during the initial runs of the static algorithm and avoids the recomputations for the nodes unaffected by the updates. Besides, motivated from the success of Graph Neural Networks (GNNs) on various graph mining problems, we also design a Graph Neural Network-based model, GNN-SHS, to discover SHSs in dynamic networks, aiming to reduce the computational cost while achieving high accuracy. We provide a theoretical analysis of the Tracking-SHS algorithm, and our theoretical results prove that for a particular type of graphs, such as Preferential Attachment graphs [1], Tracking-SHS algorithm achieves 1.6 times of speedup compared with the static algorithm. We perform extensive experiments, and our results demonstrate that the Tracking-SHS algorithm attains a minimum of 3.24 times speedup over the static algorithm. Also, the proposed second model GNN-SHS is on an average 671.6 times faster than the Tracking-SHS algorithm.