Machine learning models for sensor-based human activity recognition (HAR) are expected to adapt post-deployment to recognize new activities and different ways of performing existing ones. To address this need, Online Continual Learning (OCL) mechanisms have been proposed, allowing models to update their knowledge incrementally as new data become available while preserving previously acquired information. However, existing OCL approaches for sensor-based HAR are computationally intensive and require extensive labeled samples to represent new changes. Recently, pre-trained model-based (PTM-based) OCL approaches have shown significant improvements in performance and efficiency for computer vision applications. These methods achieve strong generalization capabilities by pre-training complex models on large datasets, followed by fine-tuning on downstream tasks for continual learning. However, applying PTM-based OCL approaches to sensor-based HAR poses significant challenges due to the inherent heterogeneity of HAR datasets and the scarcity of labeled data in post-deployment scenarios. This paper introduces PTRN-HAR, the first successful application of PTM-based OCL to sensor-based HAR. Unlike prior PTM-based OCL approaches, PTRN-HAR pre-trains the feature extractor using contrastive loss with a limited amount of data. This extractor is then frozen during the streaming stage. Furthermore, it replaces the conventional dense classification layer with a relation module network. Our design not only significantly reduces the resource consumption required for model training while maintaining high performance, but also improves data efficiency by reducing the amount of labeled data needed for effective continual learning, as demonstrated through experiments on three public datasets, outperforming the state-of-the-art. The code can be found here: https://anonymous.4open.science/r/PTRN-HAR-AF60/