We present a detailed stellar population analysis for a sample of 24 early-type galaxies (ETGs) belonging to the rich cluster RX J0152.7-1357 at z = 0.83. We have derived the age, metallicity, abundance pattern, and star formation history (SFH) for each galaxy individually to further characterize this intermediate-z reference cluster. We then study how these stellar population parameters depend on the local environment. This provides a better understanding on the formation timescales and subsequent evolution of the substructures in this cluster. We have also explored the evolutionary link between z ~ 0.8 ETGs and those in the local universe by comparing the trends that the stellar population parameters followed with galaxy velocity dispersion at each epoch. We find that the ETGs in Coma are consistent with being the (passively evolving) descendants of the ETG population in RX J10152.7-1357. Furthermore, our results favor a downsizing picture, where the subclumps centers were formed first. These central parts contain the most massive galaxies, which formed the bulk of their stars in a short, burst-like event at high z. On the contrary, the cluster outskirts are populated with less-massive, smaller galaxies that show a wider variety of SFHs. In general, they present extended star formation episodes over cosmic time, which seems to be related to their posterior incorporation into the cluster around 4 Gyr after the initial event of formation.