Despite the Paris Agreement, countries worldwide persist in non-harmonized and weak climate policies, triggered by concerns about competitiveness and trade effects. In view of this, the concept of a “climate club” of countries appears to be a promising complement to the Paris Agreement. This study sheds light on the potential of such a club through the use of an agent-based model that explores its dynamics and convergence to a stable coalition. The model describes 31 heterogeneous (blocks of) countries calibrated on empirical data concerning carbon emissions, abatement costs, domestic carbon prices, and the relative change in export volume upon the introduction of a border carbon tariff. In each period, non-members evaluate the possibility to join the club, while club members consider the option of leaving it, based on trading-off costs and benefits. The iterative process of joining and leaving is repeated until a stable coalition emerges in which no country wants to change its membership status. We run the model for 117 scenarios that capture a variation in the values of four key parameters: the initial coalition, the uniform carbon price of the club, the stringency of the border tariff, and the allocation of tariff revenues. An additional scenario is developed to capture the implications of WTO rules. The results indicate that achieving global coverage by a club created by the European Union alone or together with the United States has a high likelihood under a sufficiently stringent border tariff, equal to or higher than the club’s carbon price. Moreover, a partial return of the tariff revenues to non-members helping them cover abatement costs serves both to mitigate the risk of trade retaliation and to further motivate outsiders to join the club.