This paper introduces FSL-HDnn, an energy-efficient accelerator that implements the end-to-end pipeline of feature extraction, classification, and on-chip few-shot learning (FSL) through gradient-free learning techniques in a 40 nm CMOS process. At its core, FSL-HDnn integrates two low-power modules: Weight clustering feature extractor and Hyperdimensional Computing (HDC). Feature extractor utilizes advanced weight clustering and pattern reuse strategies for optimized CNN-based feature extraction. Meanwhile, HDC emerges as a novel approach for lightweight FSL classifier, employing hyperdimensional vectors to improve training accuracy significantly compared to traditional distance-based approaches. This dual-module synergy not only simplifies the learning process by eliminating the need for complex gradients but also dramatically enhances energy efficiency and performance. Specifically, FSL-HDnn achieves an Intensity unprecedented energy efficiency of 5.7 TOPS/W for feature 1 extraction and 0.78 TOPS/W for classification and learning Training Intensity phases, achieving improvements of 2.6X and 6.6X, respectively, Storage over current state-of-the-art CNN and FSL processors.