As a Wyoming National Guard member you are exempt from serving as a juror, from labor on public highways, and from garnishment of the wages you earn for Guard service. On state active duty you cannot be held personally liable for lawful acts performed in your official duties, and the state pays for legal counsel if a civil action is brought against you. Also on state active duty, you can practice a licensed profession, skill or trade without holding a Wyoming license or certification, provided you meet the Wyoming National Guard requirements.
There is nothing to apply for. Raise the exemption directly with the court, your employer or the licensing body, and contact your unit judge advocate or the Wyoming Military Department if you need it asserted for you.
Proof of Wyoming National Guard membership, plus your state active duty orders where the protection depends on being on state active duty.