Context. In the era of large spectroscopic surveys, massive databases of high-quality spectra coupled with the products of the Gaia satellite provide tools to outline a new picture of our Galaxy. In this framework, an important piece of information is provided by our ability to infer stellar ages, and consequently to sketch a Galactic timeline. Aims. We aim to provide empirical relations between stellar ages and abundance ratios for a sample of stars with very similar stellar parameters to those of the Sun, namely the so-called solar-like stars. We investigate the dependence on metallicity, and we apply our relations to independent samples, that is, the Gaia-ESO samples of open clusters and of field stars. Methods. We analyse high-resolution and high-signal-to-noise-ratio HARPS spectra of a sample of solar-like stars to obtain precise determinations of their atmospheric parameters and abundances for 25 elements and/or ions belonging to the main nucleosynthesis channels through differential spectral analysis, and of their ages through isochrone fitting. Results. We investigate the relations between stellar ages and several abundance ratios. For the abundance ratios with a steeper dependence on age, we perform multivariate linear regressions, in which we include the dependence on metallicity, [Fe/H]. We apply our best relations to a sample of open clusters located from the inner to the outer regions of the Galactic disc. Using our relations, we are able to recover the literature ages only for clusters located at RGC > 7 kpc. The values that we obtain for the ages of the inner-disc clusters are much greater than the literature ones. In these clusters, the content of neutron capture elements, such as Y and Zr, is indeed lower than expected from chemical evolution models, and consequently their [Y/Mg] and [Y/Al] are lower than in clusters of the same age located in the solar neighbourhood. With our chemical evolution model and a set of empirical yields, we suggest that a strong dependence on the star formation history and metallicity-dependent stellar yields of s-process elements can substantially modify the slope of the [s/α]–[Fe/H]–age relation in different regions of the Galaxy. Conclusions. Our results point towards a non-universal relation [s/α]–[Fe/H]–age, indicating the existence of relations with different slopes and intercepts at different Galactocentric distances or for different star formation histories. Therefore, relations between ages and abundance ratios obtained from samples of stars located in a limited region of the Galaxy cannot be translated into general relations valid for the whole disc. A better understanding of the s-process at high metallicity is necessary to fully understand the origin of these variations.