The Chemistry Camera (ChemCam) instrument onboard Curiosity can detect minor and trace elements such as lithium, strontium, rubidium, and barium. Their abundances can provide some insights about Mars' magmatic history and sedimentary processes. We focus on developing new quantitative models for these elements by using a new laboratory database (more than 400 samples) that displays diverse compositions that are more relevant for Gale crater than the previous ChemCam database. These models are based on univariate calibration curves. For each element, the best model is selected depending on the results obtained by using the ChemCam calibration targets onboard Curiosity. New quantifications of Li, Sr, Rb, and Ba in Gale samples have been obtained for the first 1000 Martian days. Comparing these data in alkaline and magnesian rocks with the felsic and mafic clasts from the Martian meteorite NWA7533—from approximately the same geologic period—we observe a similar behavior: Sr, Rb, and Ba are more concentrated in soluble‐ and incompatible‐element‐rich mineral phases (Si, Al, and alkali‐rich). Correlations between these trace elements and potassium in materials analyzed by ChemCam reveal a strong affinity with K‐bearing phases such as feldspars, K‐phyllosilicates, and potentially micas in igneous and sedimentary rocks. However, lithium is found in comparable abundances in alkali‐rich and magnesium‐rich Gale rocks. This very soluble element can be associated with both alkali and Mg‐Fe phases such as pyroxene and feldspar. These observations of Li, Sr, Rb, and Ba mineralogical associations highlight their substitution with potassium and their incompatibility in magmatic melts.