ABSTRACT This paper is the third in a series investigating, by means of N-body simulations, the implications of an initial radially anisotropic velocity distribution on the dynamics of star clusters. Such a velocity distribution may be imprinted during a cluster’s early evolutionary stages and several observational studies have found examples of old globular clusters in which radial anisotropy is still present in the current velocity distribution. Here we focus on its influence on mass segregation and the dynamics of primordial binary stars (disruptions, ejections, and component exchanges). The larger fraction of stars on radial/highly eccentric orbits in the outer regions of anisotropic clusters lead to an enhancement in the dynamical interactions between inner and outer stars that affects both the process of mass segregation and the evolution of primordial binaries. The results of our simulations show that the time-scale of mass segregation of the initially anisotropic cluster is longer in the core and shorter in the outer regions, when compared to the initially isotropic system. The evolution of primordial binaries is also significantly affected by the initial velocity distribution and we find that the rate of disruptions, ejections, and exchange events affecting the primordial binaries in the anisotropic clusters is higher than in the isotropic ones.