  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.
