ABSTRACT We present a spectrophotometric study of a mass-complete sample of quiescent galaxies at 1.0 < z < 1.3 with $\mathrm{log_{10}}(M_{\star }/\mathrm{{\rm M}_{\odot }}) \ge 10.3$ drawn from the VANDELS survey, exploring the relationship between stellar mass, age, and star-formation history. Within our sample of 114 galaxies, we derive a stellar–mass versus stellar–age relation with a slope of $1.20^{+0.28}_{-0.27}$ Gyr per decade in stellar mass. When combined with recent literature results, we find evidence that the slope of this relation remains consistent over the redshift interval 0 < z < 4. The galaxies within the VANDELS quiescent sample display a wide range of star-formation histories, with a mean quenching time-scale of 1.4 ± 0.1 Gyr. We also find a large scatter in the quenching time-scales of the VANDELS quiescent galaxies, in agreement with previous evidence that galaxies at z ∼ 1 cease star formation via multiple mechanisms. We then focus on the oldest galaxies in our sample, finding that the number density of galaxies that quenched before z = 3 with stellar masses $\mathrm{log_{10}}(M_{\star }/\mathrm{{\rm M}_{\odot }}) \ge 10.6$ is $1.12_{-0.72}^{+1.47} \times 10^{-5} \ \mathrm{Mpc}^{-3}$. Although uncertain, this estimate is in good agreement with the latest observational results at 3 < z < 4, tentatively suggesting that neither rejuvenation nor merger events are playing a major role in the evolution of the oldest massive quiescent galaxies within the redshift interval 1 < z < 3.