We present the NuSTAR extragalactic survey of the James Webb Space Telescope (JWST) North Ecliptic Pole (NEP) Time-Domain Field. The survey covers a ~0.16deg^2^ area with a total exposure of 681ks acquired in a total of nine observations from three epochs. The survey sensitivities at 20% of the area are 2.39, 1.14, 2.76, 1.52, and 5.20x10^-14^erg/cm^2^/s in the 3-24, 3-8, 8-24, 8-16, and 16-24keV bands, respectively. The NEP survey is one of the most sensitive extragalactic surveys with NuSTAR so far. A total of 33 sources were detected above 95% reliability in at least one of the five bands. We present the number counts, logN-logS, measured in the hard X-ray 8-24 and 8-16keV bands, uniquely accessible by NuSTAR down to such faint fluxes. We performed source detection on the XMM-Newton and Chandra observations of the same field to search for soft X-ray counterparts of each NuSTAR detection. The soft band positions were used to identify optical and infrared associations. We present the X-ray properties (hardness ratio and luminosity) and optical-to-X-ray properties of the detected sources. The measured fraction of candidate Compton-thick (NH>=10^24^cm^-2^) active galactic nuclei, derived from the hardness ratio, is between 3% to 27%. As this survey was designed to have variability as its primary focus, we present preliminary results on multi-epoch flux variability in the 3-24keV band.