Young's modulus is: the ratio of the stress along an axis to the strain along that axis in the range of stress in which Hooke's law holds. The shear modulus describes the material's response to shear stress. If you know Poisson's ratio it is possible to calculate Young's modulus from shear modulus. The difficulty is to measure shear strain γ in direct shear test, because the strain is not a constant over sample height.
Constant shear strain over sample height you can measure in simple shear test.
A method to get young's modulus is the oedometer test.