Clo-HDnn is an on-device learning (ODL) accelerator designed for emerging continual learning (CL) tasks. Clo-HDnn integrates hyperdimensional computing (HDC) along with low-cost Kronecker HD Encoder and weight clustering feature extraction (WCFE) to optimize accuracy and efficiency. Clo-HDnn adopts gradient-free CL to efficiently update and store the learned knowledge in the form of class hypervectors. Its dual-mode operation enables bypassing costly feature extraction for simpler datasets, while progressive search reduces complexity by up to 61% by encoding and comparing only partial query hypervectors. Achieving 4.66 TFLOPS/W (FE) and 3.78 TOPS/W (classifier), Clo-HDnn delivers 7.77x and 4.85x higher energy efficiency compared to SOTA ODL accelerators.