Among the many potential applications of topological insulator materials, their broad potential for the development of novel tunable plasmonics at THz and mid-infrared frequencies for quantum computing, terahertz detectors, and spintronic devices is particularly attractive. The required understanding of the intricate relationship between nanoscale crystal structure and the properties of the resulting plasmonic resonances remains, however, elusive for these materials. Specifically, edge- and surface-induced plasmonic resonances, and other collective excitations, are often buried beneath the continuum of electronic transitions, making it difficult to isolate and interpret these signals using techniques such as electron energy-loss spectroscopy (EELS). Here we focus on the experimentally clean energy-gain EELS region to characterise collective excitations in the topologically insulating material Bi₂Te₃ and correlate them with the underlying crystalline structure with nanoscale resolution. We identify with high significance the presence of a distinct energy-gain peak around −0.8eV, with spatially-resolved maps revealing that its intensity is markedly enhanced at the edge regions of the specimen. Our findings illustrate the reach of energy-gain EELS analyses to accurately map collective excitations in quantum materials, a key asset in the quest towards new tunable plasmonic devices.