Molecular dynamics simulations were performed on a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C₁₂mim][PF₆]) ionic liquid crystal (ILC) with the application of an oscillatory shear. We found that the oscillatory shear can both accelerate and suppress mesophase formation depending on shear amplitude. A small amplitude shear can speed up the mesophase transition dynamics and result in a more ordered mesomorphic structure than that without shear, i.e., an effect of accelerated aging. The mesophase is destabilized when the shear amplitude is large enough, resulting in a smectic A (SmA) to liquid or a smectic B (SmB) to SmA transition, with the mesophase behaviour summarized in an out-of-equilibrium phase diagram. Inside the layer plane a medium-range hexatic order was observed, with the correlation length extending to several nanometres in the shear-induced SmA phase. We rationalize the nonequilibrium mesophase behaviour from the rheology of isotropic liquids, finding a temperature-independent critical relaxation time for the mesophase transition in the translational or rotational dynamics. This finding can be used to predict the mesophase behaviour in the sheared ILCs from the rheology of isotropic liquids.