Optical emissions associated with Terrestrial Gamma-ray Flashes (TGFs) have recently become important subjects in space-based and ground-based observations since these emissions play crucial roles in understanding the generation of TGFs during thunderstorms. In this paper, we present the first time-resolved leader spectra of the optical component associated with a downward TGF. The TGF was observed at the Telescope Array Surface Detector (TASD) simultaneously with other lightning detectors, including a Lightning Mapping Array (LMA), an INTerFerometer (INTF), a Fast Antenna (FA), and a spectroscopic system. The spectroscopic system recorded leader spectra at 29,900 frames per second (33.44 $\mu$s time resolution), covering a spectral range from 400 nm to 900 nm, with 2.1 nm per pixel. The recordings of the leader spectra began 11.7 ms before the $-18$ kA return stroke and at a height of 2.37 km above the ground. These spectra reveal that optical emissions of singly-ionized nitrogen and oxygen occur between 167 $\mu$s before and 267 $\mu$s after the TGF detection, while optical emissions of neutrals (H I, 656 nm; N I, 744 nm, and O I, 777 nm) occur right at the moment of the detection. The time-dependent spectra reveal differences in the optical emissions of lightning leaders with and without downward TGFs.