We make use of the Gaia-unWISE quasar catalogue, Quaia, to constrain the growth history out to high redshifts from the clustering of quasars and their cross-correlation with maps of the Cosmic Microwave Background (CMB) lensing convergence. Considering three tomographic bins, centred at redshifts z̅i
= [0.69, 1.59, 2.72], we reconstruct the evolution of the amplitude of matter fluctuations σ
8(z) over the last ∼ 12 billion years of cosmic history. In particular, we make one of the highest-redshift measurements of σ
8 (σ
8(z = 2.72) = 0.22 ± 0.06), finding it to be in good agreement (at the ∼ 1σ level) with the value predicted by ΛCDM using CMB data from Planck. We also used the data to study the evolution of the linear quasar bias for this sample, finding values similar to those of other quasar samples, although with a less steep evolution at high redshifts. Finally, we study the potential impact of foreground contamination in the CMB lensing maps and, although we find evidence of contamination in cross-correlations at z ∼ 1.7 we are not able to clearly pinpoint its origin as being Galactic or extragalactic. Nevertheless, we determine that the impact of this contamination on our results is negligible.