Grace period auto insurance after buying an additional car

I have a full comprehensive insurance with a big auto insurance company and I want to buy a used car, Am I entitled to get a grace period of 30 days from date of purchase

In most cases insurance companies do give you a window to transfer a new vehicle to your plan. In my experience the policy will match the same coverage for up to 14-30 days that your plan currently provides for the vehicle you are replacing. For more specific information I would contact your company.