Aims. We conducted a spectral and temporal analysis of X-ray data from the Be X-ray binary pulsar SXP 15.6 located in the Small Magellanic Cloud based on NuSTAR, NICER, and Swift observations during the 2021 outburst. Methods. We present the broadband X-ray spectra of the system based on simultaneous NuSTAR and NICER observations for the first time. Moreover, we used monitoring data to study the spectral and temporal properties of the system during the outburst. Results. Comparison of the evolution of the 2021 outburst with archival data reveals a consistent pattern of variability, with multiple peaks occurring at time intervals similar to the orbital period of the system (∼36 d). Our spectral analysis indicates that most of the energy is released at high energies above 10 keV, while we found no cyclotron absorption line in the spectrum. Analysing of the spectral evolution during the outburst, we find that the spectrum is softer when brighter, which in turn reveals that the system is probably in the super-critical regime in which the accretion column is formed. This places an upper limit on the magnetic field of the system of about 7 × 1011 G. The spin-evolution of the neutron star (NS) during the outburst is consistent with an NS with a low magnetic field (∼5 × 1011 G), while there is evident orbital modulation that we modelled, and we derived the orbital parameters. We found the orbit to have a moderate eccentricity of ∼0.3. Our estimates of the magnetic field are consistent with the lack of an electron cyclotron resonance scattering feature in the broadband X-ray spectrum.