CsCr₃Sb₅, a unique kagome superconductor exhibiting clear characteristics of strong electronic correlations, has attracted significant attention. Its rich temperature-pressure phase diagram hosts intertwined orders, including two density-wave-like phases and pressure-induced superconductivity, positioning it as an ideal platform to investigate the intricate interplay between coexisting and competing quantum orders. At approximately 30 K-the temperature we denote as T₃-a possible anomaly appears as a hump in resistivity, though its origin remains largely unexplored due to limited corroborating evidence from other experimental probes. In this work, we performed systematic magnetotransport measurements under hydrostatic pressure to elucidate the nature of this anomaly. Our results reveal a wealth of intriguing magnetotransport signatures below T₃, including a nontrivial temperature dependence of the Hall coefficient, multi-band characteristics, and pressure-enhanced anomalous-Hall-like effect. Notably, these features resemble those observed in the charge-density-wave state in its sister compound CsV₃Sb₅. Our findings suggest the possibility of an additional, exotic electronic order in CsCr₃Sb₅, motivating further comprehensive investigations.