This work presents a novel 7 DOF geometrically exact shell formulation that describes through thickness stretching using a five-parameter extensible director field. Unlike conventional resultant-based shell models, the director is defined throughout the shell domain rather than solely on the mid-surface, which brings the kinematics conceptually closer to a three-dimensional solid element while retaining the rigor in rotation treatment from geometrically exact shell theory. The model directly incorporates fully three-dimensional hyperelastic constitutive relations without any stress-state assumptions, thereby enables its applications with complicated nonlinear materials models. Membrane, shear, and bending locking are mitigated using a higher order Mixed Interpolation of Tensorial Components (MITC) scheme, while thickness locking is inherently avoided through the asymmetric through thickness deformation afforded by the five-parameter extensible director. Three formulation variants—full, reduced, and uniform thickness-extension—are systematically compared via a suite of numerical examples. Results show that the full formulation, which fully accounts for the influence of the fifth director parameter on all strain components, delivers superior accuracy, robustness, and convergence, especially for incompressible or nearly incompressible materials and in thick shell analyses. The proposed model thus offers a versatile and physically transparent framework for the finite element analysis of shells undergoing large deformations and complex material behaviour.