Upon deployment to edge devices, it is often desirable for a model to further learn from streaming data to improve accuracy. However, extracting representative features from such data is challenging because it is typically unlabeled, non-independent and identically distributed (non-i.i.d), and is seen only once. To mitigate this issue, a common strategy is to maintain a small data buffer on the edge device to hold the most representative data for further learning. As most data is either never stored or quickly discarded, identifying the most representative data to avoid significant information loss becomes critical. In this paper, we propose an on-device framework that addresses this issue by condensing incoming data into more informative samples. Specifically, to effectively handle unlabeled incoming data, we propose a pseudo-labeling technique designed for unlabeled on-device learning environments. Additionally, we develop a dataset condensation technique that only requires little computation resources. To counteract the effects of noisy labels during the condensation process, we further utilize a contrastive learning objective to improve the purity of class data within the buffer. Our empirical results indicate substantial improvements over existing methods, particularly when buffer capacity is severely restricted. For instance, with a buffer capacity of just one sample per class, our method achieves an accuracy that outperforms the best existing baseline by 58.4% on the CIFAR-10 dataset.