Human activity recognition (HAR) is a research field that employs Machine Learning (ML) techniques to identify user activities. Recent studies have prioritized the development of HAR solutions directly executed on wearable devices, enabling the on-device activity recognition. This approach is supported by the Tiny Machine Learning (TinyML) paradigm, which integrates ML within embedded devices with limited resources. However, existing approaches in the field lack in the capability for on-device learning of new HAR tasks, particularly when supervised data are scarce. To address this limitation, our paper introduces Dendron, a novel TinyML methodology designed to facilitate the on-device learning of new tasks for HAR, even in conditions of limited supervised data. Experimental results on two public-available datasets and an off-the-shelf device (STM32-NUCLEO-F401RE) show the effectiveness and efficiency of the proposed solution.