We investigate electrically controllable Chern topology in a two-dimensional compensated (d)-wave altermagnet described by a lattice-regularized Bernevig–Hughes–Zhang model. In the altermagnetic reference state, the two Kramers sectors acquire momentum-dependent spin splitting and opposite sector Chern numbers, while the combined C_4zT symmetry enforces a vanishing total charge Chern number. We show that this hidden topological structure can be activated by orbital-selective magnetic coupling and independently tuned by ferroelectric orbital hybridization. The magnetic coupling removes the sector cancellation and generates C=±1 and ±2 phases, whereas the polar distortion shifts the Dirac gap closing away from high-symmetry momenta and enables electrical transitions such as C=0→-1 and C=1→2. The resulting phases exhibit the expected chiral edge-state multiplicity and quantized anomalous Hall conductivity. Their topology is further reflected in the orbital magnetization through the in-gap relation ∂_μ widetilde M_z=-C. Finally, we show that the Chern phases remain robust against transverse Kramers-sector mixing and symmetry-allowed inversion-asymmetric spin–orbit coupling. These results establish a symmetry-based route to electrically tunable Chern insulating phases in compensated altermagnets.