After completion of each race you will be asked if you want to Repair or service your car.

Repair: To repair, just use the repair menu. This menu contains options to repair different parts of your car. But do remember that each repair costs money. so use your funds wisely.
Service: After you have raced with the same car a few times, you can service it if needed. To service the car, tap on the Service option and then on any of the options such as Tires, Oil, Brakes, and Suspension.

Upgrade: You can also Updrade your car if you do not wish to buy a new one. Engine, Brakes, Tyres, Drivetrain etc. can all be upgraded. Once you have selected the upgrade, you can swipe through the different options available and select accordingly.