ABSTRACT We cross-correlate maps of the thermal Sunyaev–Zeldovich (tSZ) Compton-y parameter published by Planck with the projected distribution of galaxies in a set of low-redshift tomographic bins. We use the nearly full-sky 2MASS Photometric Redshift and WISE × SuperCOSMOS public catalogues, covering the redshift range z ≲ 0.4. Our measurements allow us to place constraints on the redshift dependence of the mass–observable relation for tSZ cluster count analyses in terms of the so-called hydrostatic mass bias parameter $1-b_{\scriptscriptstyle \rm H}$. These results can also be interpreted as measurements of the bias-weighted average gas pressure 〈bPe〉 as a function of redshift, a quantity that can be related to the thermodynamics of gas inside haloes and used to constrain energy injection processes. We measure $1-b_{\scriptscriptstyle \rm H}$ with $∼ \!13{{\ \rm per\ cent}}$ precision in six equispaced redshift bins, and find no evidence for a redshift-dependent mass bias parameter, in agreement with previous analyses. Our mean value of $1-b_{\scriptscriptstyle \rm H}= 0.59± 0.03$ is also in good agreement with the one estimated by the joint analysis of Planck cluster counts and cosmic microwave background anisotropies. Our measurements of 〈bPe〉, at the level of $∼ \!10{{\ \rm per\ cent}}$ in each bin, are the most stringent constraints on the redshift dependence of this parameter to date, and agree well both with previous measurements and with theoretical expectations from shock-heating models.