Despite the ubiquity of recombination processes in nature and various technologies, presently little is known about the dynamics of these processes. This article reports on a quasi-classical trajectory study of the dynamics of the direct three-body recombination of Cs(+) and Br(-) ions in the presence of a Xe atom at energies of the ion encounter and that of the third body ranging from 0.2 to 10 eV. Several dynamical mechanisms of stabilization of the recombining ion pair have been found. Head-on ion encounters are characterized by two mechanisms of removing the energy from the recombining pair. In the case of nonzero impact parameters of ion encounters, the dynamics leading to the stabilization of the nascent CsBr molecule becomes much more complicated and three new mechanisms appear. They depend mainly on the energy of the ion encounter, on the energy of the collision of the ion pair with the third body, and on the impact parameter of the ion encounter and the impact parameter of the third body. The common feature of all the three mechanisms is the transfer of a fraction of the rotational energy of the recombining pair to the third body. This transfer plays a key role in the stabilization of the molecule. The dynamical peculiarities observed are expected to be common for the recombination of the charged and neutral particles.