Standard single-image super-resolution (SR) upsamples and restores entire images. Yet several real-world applications require higher resolutions only in specific regions, such as license plates or faces, making the super-resolution of the entire image, along with the associated memory and computational cost, unnecessary. We propose a novel task, called LocalSR, to restore only local regions of the low-resolution image. For this problem setting, we propose a context-based local super-resolution (CLSR) to super-resolve only specified regions of interest (ROI) while leveraging the entire image as context. Our method uses three parallel processing modules: a base module for super-resolving the ROI, a global context module for gathering helpful features from across the image, and a proximity integration module for concentrating on areas surrounding the ROI, progressively propagating features from distant pixels to the target region. Experimental results indicate that our approach, with its reduced low complexity, outperforms variants that focus exclusively on the ROI.