  Magnetic phase transition under hydrostatic pressure in
TlCu$_{0.988}$Mg$_{0.012}$Cl$_3$ was investigated by magnetization
measurements. The parent compound TlCuCl$_3$ is a coupled spin dimer system,
which undergoes a pressure-induced quantum phase transition from a gapped
ground state to an antiferromagnetic state at $P_{\rm c} = 0.42$ kbar due to
the shrinkage of the gap. At ambient pressure, the present doped system
exhibits impurity-induced magnetic ordering at $T_{\rm N}=2.5$ K. With
increasing pressure, $T_{\rm N}$ increases. This is because the effective
exchange interaction $J_{\rm eff}$ between unpaired spins is enhanced by the
shrinkage of the gap. With a further increase in pressure, the present system
undergoes a phase transition to a uniform antiferromagnetic phase due to the
closing of the triplet gap in the intact dimers. The crossover from the
impurity-induced ordered phase to the uniform antiferromagnetic phase occurs at
$P \simeq 1.3$ kbar.
