  We study the role played by the magnetic frustration in the antiferromagnetic
phase of the organic salt \kappa-(BEDT-TTF)_ 2 Cu [N(CN)_2] Cl. Using the
spatially anisotropic triangular Heisenberg model we analyze previous and new
performed NMR experiments. We compute the 1/T_1 relaxation time by means of the
modified spin wave theory. The strong suppression of the nuclear relaxation
time observed experimentally under varying pressure and magnetic field is
qualitatively well reproduced by the model. Our results suggest the existence
of a close relation between the effects of pressure and magnetic frustration.
