We have derived elemental abundances of three field red horizontal branch stars using high-resolution (R$simeq$ 45,000), high signal-to-noise ratio (S/N $gtrsim$ 200) $H$ and $K$ band spectra obtained with the Immersion Grating Infrared Spectrograph (IGRINS). We have determined the abundances of 21 elements including $alpha$ (Mg, Si, Ca, S), odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Co, Ni), neutron-capture (Ce, Nd, Yb), and CNO group elements. S, P and K are determined for the first time in these stars. $H$ and $K$ band spectra provide a substantial number of S I lines, which potentially can lead to a more robust exploration of the role of sulfur in the cosmochemical evolution of the Galaxy. We have also derived $^{12}$C/$^{13}$C ratios from synthetic spectra of the first overtone (2$-$0) and (3$-$1) $^{12}$CO and (2$-$0) $^{13}$CO lines near 23440 AA and $^{13}$CO (3$-$1) lines at about 23730 AA. Comparison of our results with the ones obtained from the optical region suggests that the IGRINS high-resolution $H$ and $K$ band spectra offer more internally self-consistent atomic lines of the same species for several elements, especially the $alpha$ elements. This in turn provides more reliable abundances for the elements with analytical difficulties in the optical spectral range.
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