The source SXP 1323 is a peculiar high-mass X-ray binary located in the Small Magellanic Cloud. It is renowned for its rapid spin-up. We investigate for the first time broadband X-ray properties of SXP 1323 as observed by the Mikhail Pavlinsky ART-XC and eROSITA telescopes on board the Spectrum-Roentgen-Gamma observatory. Using ART-XC and eROSITA data, we produced a first broadband 1-20 keV X-ray spectrum and estimated the pulsed fraction box 8 keV. With the addition of archival XMM-Newton observations, we traced the evolution of the spin period of SXP 1323 over the last five years and found that after 2016, the source switched to a linear spin-up with a rate of -29.9 s yr^-1. The broadband X-ray spectrum is typical for accreting X-ray pulsars. It has a steep power-law index (Γ = -0.15) and an exponential cutoff energy of 5.1 keV. No significant difference between spectra obtained in states with and without pulsations were found.