  We present a detailed near-infrared chemical abundance analysis of 10 red
giant members of the Galactic open cluster NGC 752. High-resolution
(R$\simeq$45000) near-infrared spectral data were gathered with the Immersion
Grating Infrared Spectrograph (IGRINS), providing simultaneous coverage of the
complete H and K bands. We derived the abundances of H-burning (C, N, O),
$\alpha$ (Mg, Si, S, Ca), light odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Fe,
Co, Ni) and neutron-capture (Ce, Nd, Yb) elements. We report the abundances of
S, P, K, Ce, and Yb in NGC 752 for the first time. Our analysis yields solar
metallicity and solar abundance ratios for almost all of the elements heavier
than the CNO group in NGC 752. O and N abundances were measured from a number
of OH and CN features in the $H$ band, and C abundances were determined mainly
from CO molecular lines in the K band. High excitation \ion{C}{i} lines present
in both near-infrared and optical spectra were also included in the C abundance
determinations. Carbon isotopic ratios were derived from the R-branch band
heads of first overtone (2-0) and (3$-$1) $^{12}$CO and (2-0) $^{13}$CO lines
near 23440 \AA and (3-1) $^{13}$CO lines at about 23730 \AA. The CNO abundances
and $^{12}$C/$^{13}$C ratios are all consistent with our giants having
completed "first dredge-up" envelope mixing of CN-cyle products. We
independently assessed NGC 752 stellar membership from Gaia astrometry, leading
to a new color-magnitude diagram for this cluster. Applications of Victoria
isochrones and MESA models to these data yield an updated NGC 752 cluster age
(1.52 Gyr) and evolutionary stage indications for the program stars. The
photometric evidence and spectroscopic light element abundances all suggest
that the most, perhaps all of the program stars are members of the
helium-burning red clump in this cluster.
