Inspired by the idea of non-Hermitian spectral engineering and non-Hermitian skin effect, a novel, to the best of our knowledge, design for stable emission of coupled laser arrays with tunable phase locking and strong supermode competition suppression is suggested. We consider a linear array of coupled resonators with asymmetric mode coupling displaying the non-Hermitian skin effect and show that, under suitable tailoring of complex frequencies of the two edge resonators, the laser array can stably emit in a single extended supermode with tunable phase locking and with strong suppression of all other skin supermodes. The proposed laser array design offers strong robustness against both structural imperfections of the system and dynamical instabilities typical of semiconductor laser arrays.