Muon-spin-rotation (μSR) measurements under hydrostatic pressures in Tl(Cu_1−xMg_x)Cl₃. with x 0.015 were carried out in order to investigate the reported crossover from impurity-induced phase to pressure-induced phase. The spontaneous muon-spin-rotation, which indicates the existence of a long-range coherent order, is observed under pressures in zero field. With decreasing temperature in 3.1 kbar, the internal static magnetic field H_int saturates to 280 gauss, however, with increasing pressure at 2.3 K, H_int saturates to 320 gauss. This discrepancy suggests a new phase inside the ordered phase in the phase diagram.