Recent ground-based deep observations of the Universe have discovered large populations of massive quiescent galaxies at $z\sim3\!-\!5$ . With the launch of the James Webb Space Telescope (JWST), the on-board Near-Infrared Spectrograph (NIRSpec) instrument will provide continuous $0.6\!-\!5.3\,\unicode{x03BC}\,\mathrm{m}$ spectroscopic coverage of these galaxies. Here we show that NIRSpec/CLEAR spectroscopy is ideal to probe the completeness of photometrically selected massive quiescent galaxies such as the ones presented by Schreiber et al. (2018b, A&A, 618, A85). Using a subset of the Schreiber et al. (2018b, A&A, 618, A85) sample with deep Keck/MOSFIRE spectroscopy presented by Esdaile J., et al. (2021b, ApJ, 908, L35), we perform a suite of mock JWST/NIRSpec observations to determine optimal observing strategies to efficiently recover the star formation histories (SFHs), element abundances, and kinematics of these massive quiescent galaxies. We find that at $z\sim3$ , medium resolution G235M/FL170LP NIRSpec observations could recover element abundances at an accuracy of ${\sim}15\%$ , which is comparable to local globular clusters. Mimicking ZFOURGE COSMOS photometry, we perform mock spectrophotometric fitting with Prospector to show that the overall shape of the SFHs of our mock galaxies can be recovered well, albeit with a dependency on the number of non-parametric SFH bins. We show that deep high-resolution G235H/FL170LP integral field spectroscopy with a $S/N\sim7$ per spaxel is required to constrain the rotational properties of our sample at $>\!2\sigma$ confidence. Thus, through optimal grism/filter choices, JWST/NIRSpec slit and integral field spectroscopy observations would provide tight constraints to galaxy evolution in the early Universe.