If you cancel with your auto insurance provider before the end of your policy but have already paid in full through April of next year then yes, you should receive a refund for the unused portion of your policy. How a refund is calculated depends upon state laws and then also the guidelines of your insurance company per the terms of your insurance policy.

You will want to contact your current insurance company to cancel your policy and to find out what their procedure is to disperse refunds. In most cases, you will need to make this request in writing. It is also possible that you will need to provide additional information and may be subject to an early cancellation fee since you are canceling with your insurer midterm. Some states have pro-rate cancellation refunding setup.

Cancellation fees can differ depending upon the insurance company which your policy is through and state laws. Typically, there is no fee for cancellation except if it is cancelled at the insured’s request; at that point it is typically a short rate cancellation.

Here is an explanation of short rate cancellation that may help you understand better:

When the policy is terminated prior to the expiration date at the policyholder's request the earned premium charged would be more than the pro-rata earned premium. Generally, the return premium would be approximately 90 percent of the pro-rata return premium. However, the company may also establish its own short-rate schedule.

Another explanation of short rate cancellation that is a little more in-depth:

A policy termination in which the refunded premium is not proportional to the amount of time remaining in the policy period due to the fixed expenses incurred by the company. The insured will generally pay more for each day of coverage than if the policy had remained in force throughout the entire policy period.

Normally the cancellation of an auto insurance policy and the type of fee associated with it is regulated by each state and its own statute or laws so you should check with your state's insurance regulator to find out what cancellation fees insurance companies may be allowed to charge and about how refunds.

Make certain that your new auto insurance is in place before cancelling your old policy. If there is a lapse in coverage then your state may place penalties on you such as license or registration suspension, fines, etc. That is why it is better to have insurance overlap if necessary to make sure the new policy is in full effect before canceling your old car insurance policy.