Geophysical and geological observations hint for the presence in the lithospheric mantle of both active and fossil shear zones with varied past kinematics. Shear in the lithospheric mantle produces olivine crystallographic preferred orientations (CPO), which lead to dependence of the viscous behavior on the direction of the load. Yet, the role of anisotropic viscosity in the mantle is seldom considered in models of structural reactivation. Here, we present 3-D geodynamic finite-element models that quantify the strain and viscosity distribution in a lithosphere containing a fossil thrust (or extensional) mantle shear zone with variable orientation relatively to a new extensional or compressional tectonics. The results were compared to that of a fossil strike-slip mantle shear zone. The fossil olivine CPO in the shear zone produces an anisotropic response of the lithospheric mantle, which is modelled using a parameterized description of viscous anisotropy derived from polycrystal plasticity simulations. We found that CPO-induced reactivation of fossil extensional or thrust mantle shear zones is favored for dips 30-60° , with maximum strain localization if the load is normal to the trend of a fossil shear zone dipping by 45°-50°. This represents a broader range of reactivation potential than in fossil strike-slip mantle shear zones. Both fossil shear zones trending at 45° to the imposed load are reactivated regardless of their dip. For a given viscous anisotropy in the lithospheric mantle (i.e., fossil shear zone orientation), the associated strain localization in the crust is always higher under extensional reactivation, where strain rates may be up to ~100 times higher than those in the (isotropic) surrounding crust. These results imply that viscous anisotropy associated with fossil mantle shear zones plays a key role in large-scale structural reactivation during successive tectonic episodes, shaping the current lithospheric architecture, such as in the Pyrenees and Norwegian margin.