Despite widespread concern, the continuing effectiveness of networks of protected areas under projected 21st century climate change is uncertain. Shifts in species’ distributions could mean these resources will cease to afford protection to those species for which they were originally established. Using modelled projected shifts in the distributions of sub-Saharan Africa’s entire breeding avifauna, we show that species turnover across the continent’s Important Bird Area (IBA) network is likely to vary regionally and will be substantial at many sites (> 50% at 42% of IBAs by 2085 for priority species). Persistence of suitable climate space across the network as a whole, however, is notably high, with 88–92% of priority species retaining suitable climate space in ≥ 1 IBA(s) in which they are currently found. Only 7–8 priority species lose climatic representation from the network. Hence, despite the likelihood of significant community disruption, we demonstrate that rigorously defined networks of protected areas can play a key role in mitigating the worst impacts of climate change on biodiversity.