Thank you @chartl for these ideas! I’ll try to implement one of these to see what’s the outcome!
@dilsher_dhillon after having a look at the reference, it wasn’t of help because, as far as I understood, the author solely propose to estimate variability around fixed effects (indeed by adding random draws from random effects posterior distribution) for new clusters, having no actual data for these new clusters - which is not my case here (I have some new data for these new clusters, so I should go deeper than that!)