Under current emission trajectories, at least temporarily overshooting the Paris global warming limit of 1.5 °C above pre-industrial levels is a distinct possibility. Permanently exceeding this limit would substantially increase the risks of triggering several climate tipping elements with associated high-end impacts on human societies and the Earth system. It is essential to assess this risk under emission pathways that temporarily overshoot 1.5 °C. Here, we investigate the tipping risks associated with a number of policy-relevant future emission scenarios, using a stylised Earth system model that comprises four interconnected core tipping elements. We find that tipping risks until 2300 increase by 5 % for every tenth of a degree above 1.5 °C if global warming levels do not return to 1.5 °C or lower by the end of this century. If overshoots above 1.5 °C are limited in both peak temperature and duration (return below 1.5 °C in 2100), tipping risks until 2300 can be kept below 3 %. We show that achieving and maintaining at least net-zero greenhouse gas emissions is paramount to minimise tipping risks on multi-century timescales. Our results underscore that stringent emission reductions in the current decade in line with the Paris Agreement 1.5 °C limit are critical for planetary stability.