We present a detailed near-infrared chemical abundance analysis of 10 red giant members of the Galactic open cluster NGC 752. High-resolution (R similar or equal to 45000) near-infrared spectral data were gathered with the Immersion Grating Infrared Spectrograph, 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 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) (CO)-C-12 and (2-0) (CO)-C-13 lines near 23 440 angstrom and (3-1) (CO)-C-13 lines at about 23 730 angstrom. The CNO abundances and C-12/C-13 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 colour-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 programme stars. The photometric evidence and spectroscopic light element abundances all suggest that the most, perhaps all of the programme stars are members of the helium-burning red clump in this cluster.