State laws and insurance company guidelines differ so check with your insurance agent to find out for certain if your premiums could go up due to your vehicle being stolen. Your agent should be able to explain your provider's rating system to you. It could be that this one claim will not cause your rates to go up but if you have had a lot of claims made in total against your policy then your claims history could cause an overall rating increase.
Your auto insurance rates will not necessarily be raised because you are paid out for a comprehensive claim due to your car being stolen. Typically, when you have a comprehensive claim, your insurance carrier recognizes that it is normally due to something that is not your fault, and you had no control over, (i.e. theft, vandalism, hail damage, etc.) and do not raise rates. But as stated above insurance carriers guidelines can vary so find out from your specific company if your rates will rise and if so by how much.
If your rates do go up, it may be time to start shopping around for a new insurance provider. You can start car insurance shopping here with us.