We detected a giant X-ray flare from the RS CVn–type binary star UX Ari using the Monitor of All-sky X-ray Image on 2020 August 17 and started a series of Neutron star Interior Composition Explorer observations 89 minutes later. For a week, the entire duration of the flare was covered with 32 snapshot observations including the rising phase. The X-ray luminosity reached 2 × 1033 erg s−1, and the entire energy release was ∼1038 erg in the 0.5–8.0 keV band. X-ray spectra characterized by continuum emission with lines of Fe xxv Heα and Fe xxvi Lyα were obtained. We found that the temperature peaks before the flux does, which suggests that the period of plasma formation in the magnetic flare loop was captured. Using the continuum information (temperature, flux, and their delay time), we estimated the flare loop size to be ∼3 × 1011 cm and the peak electron density to be ∼4 × 1010 cm−3. Furthermore, using the line ratio of Fe xxv and Fe xxvi, we investigated any potential indications of deviation from collisional ionization equilibrium (CIE). The X-ray spectra were consistent with CIE plasma throughout the flare, but the possibility of an ionizing plasma away from CIE was not rejected in the flux rising phase.