In a traffic collision where no one contests liability, does defendant’s insurance company pay for car repair right away?

With few exceptions, the answer is yes. Normally you will get rental car reimbursement for up to 30 days while your car is in the repair shop. If you elect not to get a rental, you can seek recovery for loss of use. Usually you would get what the fair rental value for a car like yours would be while you don’t have your car.  more