This work introduces a novel variational gradient plasticity framework that addresses the limitations of classical plasticity theories incorporating non-local first-order terms, specifically the curl of the plastic strain field. Traditional elasto-plastic models combine a quadratic energy term associated with elastic strain and a dissipation term based on the norm of the plastic strain rate. However, these models fail to capture grain-size dependence of plastic behavior as experimentally observed at the microstructural scale.\cite{Hutchinson}. Gradient plasticity models enhance these formulations by introducing an intrinsic material length scale through non-local terms added to the energy functional. Yet, traditional gradient plasticity models rely on quadratic terms that smooth plastic strain gradients and prevent localization effects. In contrast, we propose a modification of the classical energy functional by replacing the quadratic regularization term with a sub-quadratic contribution. This novel approach allows for threshold effects and fundamentally alters the model's behavior through the curl of the plastic strain \cite{Lewintan,Wulfinghoff}. The curl term quantifies the degree of incompatibility in the plastic strain field, indicating the presence of internal defects or dislocations that prevent smooth deformation. Additionally, this term is closely related to the dislocation density tensor, offering a measure of dislocation numbers and distributions. This formulation influences the plastic threshold and emphasizes dislocation interactions at shear band tips and curved regions, facilitating the formation of highly localized plastic zones. Unlike classical gradient plasticity, which typically regularizes the solution, our approach enables sharper representations of shear bands. Our analysis explores the implications of this novel term on the energy landscape, threshold conditions, and localization evolution. Results highlight its capacity to model phenomena such as dislocation nucleation and the evolution of curved plastic regions with improved fidelity, providing new insights into material behavior under extreme conditions.