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We study the relationships between stellar mass, size and age within the quiescent population, using two mass-complete spectroscopic samples with $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}})>10.3$, taken from VANDELS at $1.0<z<1.3$, and LEGA-C at $0.6<z<0.8$. Using robust D$_{n}$4000 values, we demonstrate that the well-known 'downsizing' signature is already in place by $z\simeq1.1$, with D$_{n}$4000 increasing by $\simeq0.1$ across a $\simeq$ 1 dex mass interval for both VANDELS and LEGA-C. We then proceed to investigate the evolution of the quiescent galaxy stellar mass-size relation from $z\simeq1.1$ to $z\simeq0.7$. We find the median size increases by a factor of $1.9\pm{0.1}$ at $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}})=10.5$, and see tentative evidence for flattening of the relation, finding slopes of $α=0.72\pm0.06$ and $α=$ $0.56\pm0.04$ for VANDELS and LEGA-C respectively. We finally split our sample into galaxies above and below our fitted mass-size relations, to investigate how size and D$_{n}$4000 correlate. For LEGA-C, we see a clear difference, with larger galaxies found to have smaller D$_{n}$4000 at fixed stellar mass. Due to the faintness and smaller numbers of the VANDELS sample, we cannot confirm whether a similar relation exists at $z\simeq1.1$. We consider whether differences in stellar age or metallicity are most likely to drive this size-D$_{n}$4000 relation, finding that any metallicity differences are unlikely to fully explain the observed offset, meaning smaller galaxies must be older than their larger counterparts. We find the observed evolution in size, mass and D$_{n}$4000 across the $\simeq2$ Gyr from $z\sim1.1$ to $z\sim0.7$ can be explained by a simple toy model in which VANDELS galaxies evolve passively, whilst experiencing a series of minor mergers.