You can subtract military pay from your Illinois income if it is part of your federal adjusted gross income. That covers pay for service in the U.S. Armed Forces including basic training, pay as a cadet at a service academy or in a Reserve Officer Training Corps program, and pay for service in the National Guard or the Reserves, including a National Guard unit of another state. You cannot subtract military income that was already left out of your federal adjusted gross income, such as combat pay, and you cannot subtract Voluntary Separation Incentive pay.
There is nothing to apply for. Claim the subtraction on your Illinois income tax return, following Illinois Department of Revenue Publication 102 for military personnel.
Your Form W-2 and Leave and Earnings Statements showing the military pay you are subtracting.