We present the results of the broadband timing and spectral analysis of the poorly understood SMC pulsar RX J0032.9-7348 (=SXP 7.02) using NuSTAR and NICER observations during its X-ray brightening in 2024. Our timing analysis revealed a pulsation period of approximately 7.02 s in the X-ray light curve. The pulse profile obtained in the broad energy range is double-peaked and asymmetric in nature and shows moderate variation with the energy. An absorbed power-law model describes the 0.5-8 keV NICER spectra well. The 3-50 keV NuSTAR spectrum is best described with an absorbed power-law modified with a high-energy cutoff model. We find no evidence of iron or cyclotron line features in the energy spectrum. During our observation period, the 0.5-50 keV luminosity varies in the range of erg s. We also discuss the dependence of spectral parameters on the rotational phase of the pulsar through phase-resolved spectroscopy.