Identifying methods to further push the boundaries of existing low-power designs has gained new traction, driven by the wide-scale use of large language models. Graphene is well-suited for ultra-low-power nano-electronics due to its exceptional characteristics like ballistic transport, flexibility, and bio-compatibility. In this paper we investigate the feasibility of using ultra-low-voltage GNR structures, in conjunction with power reduction techniques to implement a GNR-based current-starved ring oscillator. By exploiting their low operating voltage and attofarad range intrinsic capacitances we achieve a 1.89 x higher output frequency while simultaneously reducing the power consumption by 553.8 x and achieving a 812 x higher power efficiency.