Unilateral climate policies have been unable to achieve intended emissions reductions. We argue that international harmonization of climate policy beyond the Paris Agreement is the only way forward and that global carbon pricing, either through a tax or market, is the best available instrument to manage this. A foundation has already been laid, as current carbon pricing initiatives cover about 20% of global CO2 emissions. Since it limits free-riding by countries/jurisdictions, global carbon pricing is, in principle, behaviourally easier to negotiate than other instruments, such as emission targets or technical standards. To overcome political resistance, we propose a dynamic strategy consisting of two parallel tracks and five transition phases. The first track entails assembly of a carbon-pricing coalition that expands over time and exerts moral and economic pressure on non-members to join. The second track involves refocusing UN intergovernmental climate change negotiations on carbon pricing, potentially involving initially heterogeneous prices reflecting distinct income levels of countries, which then gradually converge. The dual tracks are designed to reinforce one another, increasing the likelihood of a successful outcome. The proposal results in a transition trajectory consisting of two interactive tracks and five phases, with specific attention to inequity within and among countries. We illustrate how such an approach could function with either a carbon tax or market.