Fish contribute to the export of carbon out of the euphotic zone. They ingest organic carbon fixed by phytoplankton, store it in their tissues for their lifetime, and contribute to long-term sequestration by producing sinking fecal pellets, respiring at depth, or via their own sinking carcasses. While the flux of carbon through fish is small relative to the export flux by plankton, humans have a direct influence on fish communities and thus on the magnitude of carbon storage and flux. We use a size spectrum model to examine the combined effect of fishing and trophic dynamics on the total carbon stored as biomass of a simulated community of fish. By sampling 10,500 possible fishing strategies that randomize fishing mortality and size-selectivity, we consider optimal strategies that balance several UN Sustainable Development Goals addressing (1) food security, (2) climate action, and (3) marine conservation. The model shows that fishery management strategies that preferentially conserve large species increase overall carbon stored in the fish community. This study presents a perspective for considering carbon storage and sequestration in fisheries management alongside alternative objectives such as food production and biodiversity conservation. Our study focused on the state (total carbon in the living community). Incorporating rate processes like fecal pellet flux, vertical migration, and natural mortality would build toward a more holistic carbon approach to fisheries management.