Context. Sites for next-generation telescopes are chosen decades before the first light of a telescope. Site selection is usually based on recent measurements over a period that is too short to account for long-term changes in observing conditions such as those arising from anthropogenic climate change. For astronomical facilities with a typical lifetime of 30 yr, it is therefore essential to be aware of climate evolution to optimise observing time. Aims. In this study, we analyse trends in astronomical observing conditions for eight sites. Most sites either already host telescopes that provide in situ measurements of weather parameters or are candidates for hosting next-generation telescopes. For a fine representation of orography, we use the highest resolution global climate model (GCM) ensemble available provided by the high-resolution model intercomparison project and developed as part of the European Union Horizon 2020 PRIMAVERA project. Methods. We evaluate atmosphere-only and coupled PRIMAVERA GCM historical simulations against in situ measurements and the fifth generation atmospheric reanalysis (ERA5) of the European centre for medium-range weather forecasts for the period 1979–2014. The projections of changes in current site conditions are then analysed for the period 2015–2050 using PRIMAVERA future climate simulations. Results. Over most sites, we find that PRIMAVERA GCMs show a good agreement in temperature, specific humidity, and precipitable water vapour compared to in situ observations and ERA5. The ability of PRIMAVERA to simulate those variables increases confidence in their projections. For those variables, the model ensemble projects an increasing trend for all sites, which will result in progressively poorer astronomical observing conditions compared to current conditions. On the other hand, no significant trends are projected for relative humidity, cloud cover, or astronomical seeing and PRIMAVERA does not simulate these variables well compared to observations and reanalyses. Therefore, there is little confidence in these projections. Conclusions. Our results show that climate change will negatively impact the quality of astronomical observations and is likely to increase time lost due to bad site conditions. We stress that it is essential for astronomers to include long-term climate projections in their process for site selection and monitoring. We show that high-resolution GCMs can be used to analyse the effect of climate change on site characteristics of next-generation telescopes.