A new Reynolds stress anisotropy closure that includes nonlocal and nonequilibrium effects in turbulent flows has been obtained from a recently proposed nonlocal anisotropy formulation. This formulation is based on a new nonlocal derivation of the rapid pressure-strain correlation, which rigorously accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gradient tensor. The present nonlocal and nonequilibrium anisotropy model is obtained as a quasi-linear solution to the anisotropy transport equation, and directly replaces the classical local equilibrium Boussinesq closure in standard two-equation turbulence models. This allows straightforward implementation of the present approach in existing computational frameworks for solving the Reynolds averaged Navier-Stokes equations. Here we present the first assessment of the model in inhomogeneous flows - where nonlocal effects are expected to be important - by comparing with results from direct numerical simulations of turbulent channel flow.