The oldest stars in the Milky Way are metal-poor with Fe/H $<$ -- 1.0, displaying peculiar elemental abundances compared to solar values. The relative variations in the chemical compositions among stars is also increasing with decreasing stellar metallicity, allowing for the pure signature of unique nucleosynthesis processes to be revealed. The study of the $r$-process is, for instance, one of the main goals of stellar archaeology and metal-poor stars exhibit an unexpected complexity in the stellar production of the $r$-process elements in the early Galaxy. In this work, we report the atmospheric parameters, main dynamic properties, and the abundances of four metal-poor stars: HE 1523-–0901, HD 6268, HD 121135, and HD 195636 (--1.5 $>$ Fe/H The abundances were derived from spectra obtained with the HRS echelle spectrograph at the Southern African Large Telescope, using both local and non-local thermodynamic equilibrium (LTE and NLTE) approaches, with the average error between 0.10 and 0.20 dex. Based on their kinematical properties, we show that HE 1523--0901 and HD 195636 are halo stars with typical high velocities. In particular, HD 121135 displays a peculiar kinematical behaviour, making it unclear whether it is a halo or an accreted star. Furthermore, HD 6268 is possibly a rare prototype of very metal-poor thick disk stars. The abundances derived for our stars are compared with theoretical stellar models and with other stars with similar metallicity values from the literature. HD 121135 is Al-poor and Sc-poor, compared to stars observed in the same metallicity range (--1.62 $>$ Fe/H $>$--1.12). The most metal-poor stars in our sample, HE 1523 -- 0901, HD 6268, and HD 195636, exhibit anomalies that are better explained by supernova models from fast-rotating stellar progenitors for elements up to the Fe group. Compared to other stars in the same metallicity range, their common biggest anomaly is represented by the low Sc abundances. If we consider the elements beyond Zn, HE 1523--0901 can be classified as an r-II star, HD 6268 as an r-I candidate, and HD 195636 and HD 121135 exhibiting a borderline $r$-process enrichment between limited-r and r-I star. Significant relative differences are observed between the $r$-process signatures in these stars.