We investigate the possibility of the electrical control of spin transfer in monoatomic chains incorporating spin impurities. Our theoretical framework is the mixed quantum-classical (Ehrenfest) description of the spin dynamics, in the spirit of thes-d model, where the itinerant electrons are described by a tight-binding model while localized spins are treated classically. Our main focus is on the dynamical exchange interaction between two well-separated spins. This can be quantified by the transfer of excitations in the form of transverse spin oscillations. We systematically study the effect of an electrostatic gate bias V_g on the interconnecting channel and we map out the long-range dynamical spin transfer as a function of V_g. We identify regions of V_g giving rise to significant amplification of the spin transmission at low frequencies and relate this to the electronic structure of the channel.