When I parked a car and after leaving time my car is damaged then valet service provider provide me the facilities of servicing,repairing.

If you entrusted your car to a valet parking service, then they should be responsible for any damage caused while in their care.

They should pay for the damages, not do the actual repair. But you will need to have shown them the damage, and they may challenge it. So be prepared to sue if needed.