A car with a skid trace behind it, meaning electronic stability control is intervening or unavailable.
Can you continue driving?
Yes, with caution — get it checked soon

Electronic stability control is either intervening right now (flashing) or unavailable (steady). ESC is the system that detects a slide beginning and brakes individual wheels to correct it, usually before the driver has registered anything is wrong.
Flashing: reduce speed and make your steering inputs smooth. The car is already working at the limit of grip.
Steady: you are driving without the safety net. Slow down in wet, cold or loose conditions and avoid sudden steering or lifting off mid-corner.
Soon. Stability control is among the most effective safety systems ever fitted to cars, and driving for weeks without it is a poor trade for a repair that is usually straightforward.