As a unique kagome superconductor displaying clear signatures of strong electronic correlations, CsCr3Sb5 has drawn much attention. Its rich temperature-pressure phase diagram features intertwined orders including pressure-induced superconductivity and two density-wave-like phases, making it an outstanding platform to explore the complex coexistence and competition of multiple quantum orders. At around 30 K, which we designate as T3, a possible anomaly manifesting as a hump in the resistivity has been observed, yet its nature remains largely unexplored due to limited supporting evidence from other probes. Here, we conducted systematic magnetotransport experiments under hydrostatic pressure to investigate the nature of this anomaly. Our results reveal an abundance of intriguing magnetotransport signatures below T3, including a non-trivial temperature dependence of the Hall coefficient, multi-band characteristics, and pressure-enhanced anomalous-Hall-like effect. These signatures bear resemblance to those observed in many other correlated materials with distinct origins. These findings suggest the possibility of an additional electronic order in CsCr3Sb5, calling for further detailed investigations.