One of the main causes for degradation of the insulating components of electric cables is the Electrical Treeing, a gas-filled fracture generated by the interaction of Partial Discharges (PD) with the polymeric surface under the prolonged action of intense electrical fields. This phenomenon can by modeled by a system of PDEs [4], describing the movement of charges in the defect and the evolution of the electric field and potential in both the gas and the solid dielectric material. The geometry of the Electrical Treeing consists in a ramification with very small diameter, requiring an extremely fine 3D mesh. To overcome the limitations due to computational costs, we approximate the treeing as a one-dimensional graph, and derive a mixed-dimensional 3D-1D system of equations, reducing the problem complexity. We derive a one-dimensional model for the charge concentrations in the gas, coupled with a 3D-1D model for the electrostatics, derived in [2], following a similar approach to [1] but with some differences due to the specific features of the problems. This way, we can directly compute the electric field and potential in the 3D insulator, but only the component of the electric field in the gas along the direction of the 1D domain, while its transversal components are treated aposteriori by superimposition of the effects of all the charge concentrations and of the possible presence of an external electric field. The numerical solution of the electrostatic problem is based on mixed FEM in the 3D domain and FEM on the 1D graph, while for the movement of charges in the gas we employ an ad hoc solver [3], based on Finite Volumes on graphs, with implicit time discretization. We validate the 3D-1D electrostatic model on simple geometries and test both problems on the geometry of a realistic Electrical Treeing, gaining drastic reduction in the computational cost. Moreover, the reduction to one dimension of the gas domain allows simulations on more complex geometries, where 3D meshes can hardly be generated.