  Recent ground-based deep observations of the Universe have discovered large
populations of massive quiescent galaxies at z~3-5. With the launch of the
James Webb Space Telescope (JWST), the on-board NIRSpec instrument will provide
continuous 0.6-5.3 $\mu$ 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). Using a subset of the Schreiber et al. (2018b)
sample with deep Keck/MOSFIRE spectroscopy presented by Esdaile et al. (2020),
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~3, medium resolution G235M/FL170LP NIRSpec observations could
recover element abundances at an accuracy of ~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~7 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.
