Single-atom catalysts have attracted extensive attention for the electrochemical nitrate reduction reaction (NO₃RR). However, effective catalyst design principles, particularly transferable activity descriptors across different structures, remain limited. Based on single-atom systems supported on chiral carbon nanotubes (CNTs), a total of 71 SAC models were constructed, comprising different metal centers, coordination environments, and CNT diameters. After stability, nitrate-adsorption, and selectivity screening, 45 systems were selected for complete free-energy pathway calculations. Our results show that V-C₂N₂/CNT and Os-C₂N₂/CNT exhibit favorable catalytic performance with limiting potentials of -0.36 and -0.37 V. A consistent volcano-type relationship was identified between catalytic activity and the adsorption energy of NO₃^-. This relationship remains consistent across different doping configurations and CNT sizes. The adsorption energy of NO₃^- exhibits a linear relationship with key intermediate species, providing a thermodynamic rationale for using nitrate adsorption energy as an activity descriptor. Machine-learning analysis identifies the valence-electron count and local TM–N coordination as influential features for predicting ΔG_*NO3 within the present dataset. These findings provide useful insights into the design of chiral-CNT-supported NO₃RR catalysts.