The NCB (No Claim Bonus) will not be transferred to the buyer of your old car, as it is available to the person/you and not the car. Therefore, it will be carried forward to your new car's insurance. This is available even if the insurance company changes. In any case, the new car should be bought/insured within 90 Days from the date of selling/transfering the old car.

When your car is sold/transferred, the insurance will also be transferred in the buyer's name. Once this is done, you are entitled to obtain 'NCB certificate' from the insurance company. Obtain the same & submit it to the insurance company (same or other) that is insuring your new car. The insurance company will extend that NCB to you for the new car insurance.