While numerous methods achieving remarkable performance exist in the Object Detection literature, addressing data distribution shifts remains challenging. Continual Learning (CL) offers solutions to this issue, enabling models to adapt to new data while maintaining performance on previous data. This is particularly pertinent for edge devices, common in dynamic environments like automotive and robotics. In this work, we address the memory and computation constraints of edge devices in the Continual Learning for Object Detection (CLOD) scenario. Specifically, (i) we investigate the suitability of an open-source, lightweight, and fast detector, namely NanoDet, for CLOD on edge devices, improving upon larger architectures used in the literature. Moreover, (ii) we propose a novel CL method, called Latent Distillation~(LD), that reduces the number of operations and the memory required by state-of-the-art CL approaches without significantly compromising detection performance. Our approach is validated using the well-known VOC and COCO benchmarks, reducing the distillation parameter overhead by 74\% and the Floating Points Operations~(FLOPs) by 56\% per model update compared to other distillation methods.