Gravity waves generated by tropical deep convection contribute significantly to driving the downward propagation of the quasi‐biennial oscillation (QBO). However, it is currently uncertain how gravity waves, their interaction with the QBO, and thus the QBO itself will respond to a warming climate. Previous work showed that this uncertainty is a consequence of the parameterization of gravity waves employed in conventional general circulation models. In this study, we therefore perform short explicit simulations of the QBO for different idealized climate states with the model ICON‐A in a deep convection‐permitting setup, which means that neither a parameterization of convection nor a parameterization of gravity waves is employed and that the QBO is entirely driven by explicitly resolved waves. Thereby, our simulations allow us to provide a very first direct estimate of how tropical gravity waves and the QBO may change in a warming climate. We found that the lower‐stratospheric gravity wave momentum flux that is relevant for the QBO increases substantially in the warmer climate states and shifts towards faster zonal phase speeds. As a consequence, the downward propagation of the QBO accelerates and the magnitude of the QBO jets in the upper QBO domain increases in the warmer climate states. Thus, our work builds an important first step toward a more comprehensive assessment of potential QBO changes using global storm‐resolving models.This article is protected by copyright. All rights reserved.