A repetitively pulsed plasma was used to stabilize a lean premixed turbulent swirl flame under flow pulsations with amplitudes ranging between 10 and 30% of the total flow rate. Flow pulsations with a frequency of 5 Hz were generated by a high-amplitude flow disturbance system to simulate the surge conditions in real combustors. The discharge pulses were set with a tunable delay time relative to the flow pulsations. When the discharge pulses occur before or during the flow pulsation, the plasma extends the lean flammability limit of the swirl flame. The transient heat-release rate indicates that the flame stabilization is caused by a plasma reignition process. However, when the plasma discharges occur with specific time delays after the flow pulsation, the plasma further destabilizes the flame, which is attributed to wrinkled flame surfaces and shock waves generated by plasma aerodynamic actuation. Increasing the discharge frequency to 40 Hz further extends the ignition limits from 0.63 to 0.45 due to the increased average ignition energy. The paper may provide an alternative solution for direct control of unsteady combustion dynamics.