In the present study, we explore the cosmological implications of Rényi holographic dark energy within the framework of \(f(R,T)\) gravity by considering an anisotropic Kantowski–Sachs space time. To obtain exact solutions, we employ Berman’s law corresponding to a constant deceleration parameter and assume a proportional relationship between the shear scalar and the expansion scalar. The derived model exhibits a gradual decrease in the RHDE density as the Universe evolves, eventually tending toward a finite positive value at late times. At the same time, the pressure remains negative throughout the evolution and approaches a nearly constant value in the asymptotic regime. The behaviour of the equation of state parameter indicates a transition from values near zero to more negative values, supporting the onset of accelerated expansion. Our analysis shows that the Null Energy Condition (NEC) and the Dominant Energy Condition (DEC) remain satisfied; however, the Strong Energy Condition (SEC) is violated, consistent with late-time acceleration. Statefinder diagnostics reveal that the model evolves toward the ΛCDM fixed point. Although the squared sound speed is negative, reflecting non-canonical perturbative behaviour common in modified gravity, the background evolution remains well behaved. Overall, RHDE in \(f(R,T)\) gravity provides a viable description of late-time cosmic acceleration.
