North Atlantic tropical cyclone (TC) activity exhibits considerable interannual variability, with La Niña and the positive phase of the Atlantic Meridional Mode (AMM) tending to drive active hurricane seasons, and El Niño and negative AMM often driving inactive hurricane seasons. Previous studies have largely focused on mean changes in TC activity; however, changes in the distribution of seasonal TC activity have received less attention. This study examines how active and inactive Atlantic hurricane seasons may change in the future by performing atmosphere-only simulations using the high-resolution Energy Exascale Earth System Model (E3SM). We performed simulations forced by sea-surface temperature (SST) patterns characteristic of La Niña and the positive AMM jointly, and El Niño and the negative AMM jointly, in historical and future climates. Projected Atlantic TCs become more frequent in the future by 34% during El Niño and negative AMM and by 66% during La Niña and positive AMM. Furthermore, we found a significant increase in the portion of intense TCs in the future. These responses in TC activity are related to changes in TC environmental favorability, with warmer SSTs increasing TC potential intensity, and reduced wind shear and increased mid-tropospheric humidity further supporting TC activity. This research highlights the importance of considering how future changes in both the mean climate state and climate variability can influence the active and inactive tails of the seasonal Atlantic TC activity distribution. Notably, we found that the patterns of ocean variability that drive the most active Atlantic hurricane seasons in the historical record, when paired with climate change, have the potential to produce hurricane seasons that are even more active. In addition, the patterns of ocean variability that typically suppress Atlantic TCs in the historical climate become less effective at doing so in the future. Altogether, the simulated shift in the future extremes in seasonal Atlantic TC activity represents a potential worsening of Atlantic TC impacts in the future.