In this talk, we consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. The pioneering work of Voiculescu showed that the spectral distribution of this random matrix model is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. Assuming the typical square-root behavior at the edge of the limiting free additive convolution, we show that the Voiculescu's law holds locally on the scale slightly above the local eigenvalue spacing at the edge. Together with our previous result in the bulk, this implies the optimal rigidity of the eigenvalues and optimal rate of convergence of Voiculescu's law. This talk is based on the joint work with László Erdős and Kevin Schnelli.