We propose a next-generation adaptive convection-circulation coupling framework (NextACC) to study interactions between convection and large-scale circulation. NextACC incorporates a cubed-sphere shallow water model (CSSWM) for large-scale dynamics and a two-dimensional vector vorticity equation could-resolving model (2DVVM) for convective processes. The key features of this framework are the adjustable coupling time intervals and the flexible spatial distributions for selective coupled grids. We demonstrate the framework by conducting experiments on convection-initiated large-scale gravity waves. The results show that coupling enhances convection strength, prolongs its lifespan, and intensifies large-scale gravity waves. Additionally, coupling time intervals regulate convection-circulation interactions, revealing two predominant timescales—one linked to large-scale gravity wave propagation and the other to convection lifespan. The results also suggest that faster gravity waves amplify variability during interactive periods, whereas slower waves sustain variability for longer durations during non-interactive periods. NextACC bridges the gap between general circulation models (GCMs) and global storm resolving models (GSRMs), offering an effective tool for studying convection-circulation interactions and coupling and identifying possible quasi-equilibrium states for various atmospheric phenomena.