Aspect Term Extraction (ATE) identifies aspect terms in review sentences, a key subtask of sentiment analysis. While most existing approaches use energy-intensive deep neural networks (DNNs) for ATE as sequence labeling, this paper proposes a more energy-efficient alternative using Spiking Neural Networks (SNNs). Using sparse activations and event-driven inferences, SNNs capture temporal dependencies between words, making them suitable for ATE. The proposed architecture, SpikeATE, employs ternary spiking neurons and direct spike training fine-tuned with pseudo-gradients. Evaluated on four benchmark SemEval datasets, SpikeATE achieves performance comparable to state-of-the-art DNNs with significantly lower energy consumption. This highlights the use of SNNs as a practical and sustainable choice for ATE tasks.