This article follows earlier studies on the physical origin of magnetic anisotropy and the means of controlling it in polynuclear transition metal complexes. The difficulties encountered when focusing a magnetic field on a molecular object have led to consider the electric field as a more appropriate control tool. It is therefore fundamental to understand what governs the sensitivity of magnetic properties to the application of an electric field. We have already studied the impact of the electric field on the isotropic exchange coupling and on the Dzyaloshinskii–Moriya interaction (DMI). Here, we focus on the symmetric exchange anisotropy tensor. In order to obtain significant values of anisotropic interactions, we have carried out this study on a model complex that exhibits first-order spin–orbit coupling. We will show that (i) large values of the axial parameter of symmetric exchange can be reached when close to the first-order spin–orbit coupling regime, (ii) both correlated energies and wave functions must be used to achieve accurate values of the symmetric tensor components when the DMI is non-zero, and (iii) finally, an interferential effect between the DMI and the axial parameter of symmetric exchange occurs for a certain orientation of the electric field, i.e., the latter decreases in magnitude as the former increases. While DMI is often invoked as being involved in magneto-electric coupling, isotropic exchange and the symmetrical anisotropic tensor also contribute. Finally, we provide a recipe for generating significant anisotropic interactions and a significant change in magnetic properties under an electric field.