Summary: The aim of this paper is to investigate the expansion-free model of a star cluster in modified Gauss-Bonnet gravity. To achieve this, we analyze a model of a star cluster which is dissipative, anisotropic and viscous. The modified field equations as well as junction conditions are applied in order to study the general distribution of an anisotropic fluid exhibiting dissipation with varying dominant stress components. We also integrate the condition of vanishing expansion into our analysis. To gain insight into the significance of motion that does not involve expansion, we discuss two distinct ways of defining the radial velocity of a fluid element. The study demonstrates the emergence of a cavity in the evolution of star clusters when expansion is not present. Moreover, we determine the shear-free and expansion-free collapse of the star cluster by analyzing the relative velocity among adjacent fluid layers. The Skripkin model [V. A. Skripkin, Sov. Phys., Dokl. 5, 1183-1186 (1961; Zbl 0104.44001); translation from Dokl. Akad. Nauk SSSR 135, 1072-1075 (1960)] can be used to represent an expansion-free, non-dissipative, and isotropic star cluster. This provides a valuable tool for investigating the properties and behavior of these celestial bodies. The Skripkin model demonstrates homologous evolution for the shear-free case. We conclude that the exotic matter present in \(f(G, T)\) gravity is essential for understanding the dynamics of the star cluster’s evolution. This indicates that the dark source terms should be taken into account when investigating the properties and behavior of the celestial bodies.