High-harmonic generation is the frequency upconversion of an intense femtosecond infrared laser in a material. In condensed-phase high-harmonic generation, laser-driven currents of coherently excited charge carriers map the electronic structure onto the emitted light. This promises a thus far scarcely explored potential of condensed-phase time-resolved high-harmonic spectroscopy for probing carrier dynamics. Here, we realize this potential and use time-resolved solid-state high-harmonic spectroscopy from a laser-excited methylammonium lead bromide (MAPbBr3) thin film, a key material in perovskite solar cells, for measuring carrier cooling and relaxation on femto- and picosecond time scales. Through comparison with transient absorption, we show the links between carrier dynamics and experimental observables of generated harmonics. By highlighting and understanding the interplay of these dynamics, we demonstrate transient optical control over the emission of solid-state high-harmonic generation in MAPbBr3.