We explore the properties of a new Maxwell electrodynamics coupled to a Lorentz-violating background through the presence of higher-derivative terms. Physical implications of this alternative effective theory modified by Lorentz-violating operators of mass dimension-5 are considered, such as modified dispersion relations which exhibit the vacuum birefringence phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a background time-like four-vector, \(n^{\mu }\) , the equations of motion indeed reproduce those encountered by Gambini and Pullin in the framework of loop quantum gravity . Finally, extended expressions for Maxwell-type equations are written down in the case the external Lorentz-violating four-vector is space-like.