We perform molecular dynamics simulations on a set of ionomer melts in the presence of a static, external electric field. We employ the same coarse-grained beadspring model from our previous simulations, which characterized the zero-field morphologies and dynamics of the isolated or percolated ionic aggregates observed in these systems. Here we investigate the electric field effects on these aggregates. In the linear response regime, the morphology of both isolated and percolated aggregates is unaltered because the force between the two ions at contact is much stronger than the force on an ion due to the external field. However, the same fields are strong enough to bias the local ion dynamics so that ions in the percolated systems, which contain a continuous ionic network, transition to the steady state drift regime. Furthermore, the field biases the motion of oppositely charged ions in opposite directions and decorrelates the ionic aggregates along the field direction. In the systems with isolated ionic aggregates, higher fields are required to observe the same dynamical response. Finally, we find that the conductivity is strongly influenced by the equilibrium aggregate morphologies of these systems; the ionomers with percolating ionic aggregates have the largest conductivities.