Creates the Gun Dealer Licensing Act. Provides that it is unlawful for a person to engage in the business of selling, leasing, or otherwise transferring firearms without a license issued by the Department of Financial and Professional Regulation. Provides that a dealership agent other than a dealer licensee-in-charge may act on behalf of the licensed dealership without being licensed as a dealer under the Act. Creates the Gun Dealer Licensing Board consisting of 5 members appointed by the Secretary of Financial and Professional Regulation to recommend policies, procedures, and rules relevant to the administration and enforcement of the Act. Provides that the holder of a dealership license issued under the Act may employ in the conduct of his or her business dealership agents. Establishes qualifications for obtaining dealership licenses and for being employed as a dealership agent. Establishes penalties for violations of the Act. Provides for rulemaking, including emergency rulemaking. Amends the Regulatory Sunset Act. Provides that the Act is repealed on January 1, 2028. Amends the Illinois Administrative Procedure Act. Makes conforming changes.