Using 324 numerically modelled galaxy clusters as provided by THE THREE HUNDRED project, we study the evolution of the kinematic properties of the stellar component of haloes on first infall. We selected objects with M_star > 5 × 10¹⁰ h⁻¹ M_⊙ within 3R₂₀₀ of the main cluster halo at z = 0 and followed their progenitors. We find that although haloes are stripped of their dark matter and gas after entering the main cluster halo, there is practically no change in their stellar kinematics. For the vast majority of our ‘galaxies’ – defined as the central stellar component found within the haloes that form our sample – their kinematic properties, as described by the fraction of ordered rotation, and their position in the specific stellar angular momentum−stellar mass plane j_star − M_star are mostly unchanged by the influence of the central host cluster. However, for a small number of infalling galaxies, stellar mergers and encounters with remnant stellar cores close to the centre of the main cluster, particularly during pericentre passage, are able to spin up their stellar component by z = 0.