The oceans are by far the largest carbon sink and are estimated to have absorbed roughly 40 percent of anthropogenic carbon dioxide emissions since the beginning of the industrial era. The climate services performed by the oceans can be described as an interaction between a physical and a biological carbon pump. Whereas the role of the physical carbon pump is well established, the full scale of the climate services provided by the biological carbon pump has only recently been understood. This pump is made up of services provided by different marine species, from microbes to marine mammals. Many of these species are managed under the international law of the sea and subject to the concept of Maximum Sustainable Yield (MSY). Although the MSY concept has developed since its inception, maximum generation of fish for human consumption remains the core objective according to the law of the sea. Under MSY based management, states are not required to consider the climate services represented by different marine organisms, making this regime unable to balance the interest of maximizing fish as a product against the oceans’ role in carbon sequestration. In order to make optimal use of the carbon sequestering features of marine organisms, this perspective proposes five action points. Foremost, MSY should be complemented with a new management objective: maximum carbon sequestration (MCS). Although many aspects of climate-based fisheries management remain to be explored, it appears clear that this would imply allowing stocks to recover to maintain a larger amount of biomass, increasing conservation measures for species particularly efficient in providing negative emissions, differentiation of fisheries within species as well as a new approach to ecosystem management. Climate reforming international fisheries law could make an important contribution to the operationalization of the Paris Agreement on Climate Change, as well as the UN Sustainable Development Goals. As a first step, international guidelines should be developed on how to integrate the concept of maximum carbon sequestration in fisheries management.