We present a high-resolution atmospheric retrieval of the benchmark L-type brown dwarf HR 7672 B using near-infrared spectra obtained with REACH on the Subaru Telescope. REACH combines high-contrast imaging with high-resolution spectroscopy (R~100,000), enabling detailed characterization of faint substellar companions.We model the observed spectra with a composite framework consisting of multiple components: a brown dwarf spectrum computed with ExoJAX, a telluric absorption model, a stellar speckle contamination component, and a simplified cloud model parameterized by the cloud-top pressure to account for continuum features.From the retrieval applied to the J- and H-band spectra, we identify H2O and FeH as the dominant absorbers shaping the spectral features. The observed continuum is well explained by the combined effects of molecular opacity, CIA, and optically thick clouds. The inferred cloud-top temperature suggests the possible formation of condensates such as TiO2, Al2O3, or Fe in the atmosphere of HR 7672 B.This work represents the first science demonstration of REACH for faint substellar companions and highlights the potential of combining high spectral resolution and high contrast to probe atmospheric physics and chemistry. Our results provide a foundation for future studies of directly imaged exoplanets and brown dwarfs with next-generation instruments."