Cesium–lead–bromide (CsPbBr3) is the simplest all inorganic halide perovskite. It serves as a reference material for understanding the exceptional solar cell properties of the organic–inorganic hybrid halide perovskites and is itself discussed as an alternative absorber material. Broadband dielectric spectroscopy has proven to yield an in depth understanding of charge screening mechanisms in the halide solar cell absorbers based on methylammonium and modifications hereof. For a deeper understanding of charge carrier screening, we have investigated CsPbBr3 across wide temperature (120 K–450 K) and frequency ranges. Besides the two known phase transitions at 403 K and 361 K, the dielectric data show another anomaly around 220 K, which can be interpreted as another phase transition. XRD and EPR studies confirm the presence of this anomaly, but Raman scattering spectra do not show any lattice anomalies in the vicinity of 220 K. This additional anomaly is of first order character (different transition temperatures upon cooling and heating) but hardly influences the lattice dynamics. Our broadband dielectric investigations of CsPbBr3 display the same microwave limit permittivity as for MAPbX3 (εr ≈ 30, X = Cl, Br, I, MA = CH3NH3⁺) but do not afford a second permittivity relaxation up to this frequency. Our prior assignment of the second contribution in the methylammonium compounds being due to the relaxation dynamics of the methylammonium ion as a dipole is herewith proven. Nevertheless, CsPbBr3 shows large charge carrier screening up to very high frequencies which can still play a vital role in charge carrier dynamics and exciton behaviour in this material as well.