ABSTRACT We present results from a study of TESS observations of the eclipsing dwarf nova system Z Cha, covering both an outburst and a superoutburst. We discover that Z Cha undergoes hysteretic loops in eclipse depth – out-of-eclipse flux space in both the outburst and the superoutburst. The direction that these loops are executed in indicates that the disc size increases during an outburst before the mass transfer rate through the disc increases, placing constraints on the physics behind the triggering of outbursts and superoutbursts. By fitting the signature of the superhump period in a flux-phase diagram, we find the rate at which this period decreases in this system during a superoutburst for the first time. We find that the superhumps in this source skip evolutionary stage ‘A’ seen during most dwarf nova superoutbursts, even though this evolutionary stage has been seen during previous superoutbursts of the same object. Finally, O–C values of eclipses in our sample are used to calculate new ephemerides for the system, strengthening the case for a third body in Z Cha and placing new constraints on its orbit.