Summary: The significance of the shear-free condition on the perturbative collapse of a radiating anisotropic fluid with Karmarkar condition in the formalism of \(f(\mathcal{R}, \mathcal{T})\) gravity is analyzed in this manuscript. The gravitational collapse of a spherically symmetric radiating object proceeds from an initially static regime satisfying the time dependent Karmarkar condition and is further established by a huge amount of energy dissipation in the form of heat flux. A perturbation approach is applied to get the collapse equation and the gravitational nature of our model is entirely governed by the Karmarkar condition and its boundary condition in the scheme of \(f(\mathcal{R}, \mathcal{T})\) gravity, where \(\mathcal{R}\) is the Ricci scalar and \(\mathcal{T}\) is the trace of the energy momentum tensor. Vaidya’s time-like hypersurface is smoothly matched with the interior solution, which further entitles to examine the physical viability of the spherically symmetric source. Furthermore, a viable linear \(f(\mathcal{R}, \mathcal{T})\) model is chosen to achieve the exact solution for an anisotropic radiating fluid model. Stability tests are demonstrated, indicating that our model is well-behaved. Furthermore, general relativity results have been obtained by simply taking the coupling parameter \(\chi\) to zero.