By helping achieve emissions targets more inexpensively than expected, emissions trading systems can lower political resistance to more ambitious targets, enabling deeper and faster cuts in emissions over time. Using a dynamic global partial-equilibrium carbon market model, we quantify cost savings under scenarios for emissions trading within and across countries, as well as the corresponding potential to escalate reductions if those cost savings were translated into greater mitigation.We find global use of carbon markets could allow the world to nearly double climate ambition relative to current Paris pledges (NDCs) over 2020–2035, without increasing total costs compared to a base case without international markets.Significant potential to enhance ambition remain under scenarios where market participation is limited using a “heat map” analysis of countries’ market readiness, as well as with policy uncertainty that delays climate investments. We also find that since protecting tropical forests offers so much low-cost mitigation potential, linking reduced deforestation to an international carbon market drives a majority of the potential ambition gains across the modeled scenarios. International markets, including for deforestation, play a potentially even more critical role as global ambition increases, with roughly double the volume and ten-fold the value of international transactions if countries’ Paris pledges scale up to limit warming to 2°C. Under this scenario, global use of carbon markets lowers costs by two thirds, enabling one third more reductions for the same cost as without international markets, a gain sufficient to keep options open for limiting warming to 1.5°C. High-integrity approaches for international market cooperation—as envisioned under Article 6 of the Paris Agreement and with the inclusion of tropical forests as a priority—thus merit significant policy attention as means of closing the global emissions gap.