The MHD with embedded PIC (MHD-EPIC) model makes it feasible to incorporate kinetic physics into a global simulation. Still, this requires a large enough box-shaped PIC domain to accommodate the movement and changes of the magnetic reconnection regions over time. This wastes computational resources on simulating regions with the expensive PIC model where MHD would be sufficient to describe the physics. We have developed a new MHD with Adaptively Embedded PIC (MHD-AEPIC) algorithm that couples the BATS-R-US MHD model with the new FLexible Exascale Kinetic Simulator (FLEKS) PIC code. In the new coupled model the PIC domains can move with the magnetic reconnection regions and adapt to them with an arbitrary shape. In this work, we will first introduce the algorithms for selecting the reconnection regions in the MHD model that need to be resolved with the kinetic PIC model. Then we will compare simulations obtained with MHD-EPIC using fixed PIC regions versus MHD-AEPIC employing adaptive PIC regions to verify that the new model generates reliable results. Finally, we will apply the MHD-AEPIC model to a global magnetic storm simulation and demonstrate the improved efficiency.