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Recent studies of the time-resolved Milky Way formation using asteroseismology have shown that thick disk stars could be very old (0.8 Gyr after the Big Bang, even older than the inner halo). Additionally, thick disk stars are expected to have formed from a mixed gas and offer a better site to study the chemical enrichment history. Here, we present abundance trends for about 65 metal-poor stars (•3.1 < [Fe/H] < •1.8) that are kinematically separated into thick disk, and halo, observed with the HESP spectrograph installed at HCT telescope. The sample includes 40 newly identified stars combined with 25 stars from an earlier HESP-GOMPA survey and a compilation from literature. Generally, thick disk stars show less scatter than the halo stars. The abundance trend in [Mg/Fe] as a function of metallicity remains flat for thick disk stars, indicating similar enrichment history and well-mixed ISM with only massive star contribution, whereas the halo stars show a large scatter and a declining trend in [Mg/Fe] as a function of metallicity. The [Eu/Mg] trend show a mildly increasing trend indicating some delay in the production of Eu as compared to Mg, in both halo and the thick disk stars. The scatter in the abundance trend is larger in the halo as compared to thick disk stars, indicating that the halo is formed from accretion of multiple stellar systems.