The Continuing to Serve Act clarifies and expands the Department of Defense's SkillBridge program, which helps active-duty service members transition to civilian careers. The bill specifies that the program can work with private employers, public employers, and nonprofit organizations, ensuring eligible service members know about the opportunity. It requires the military branches to annually inform active-duty personnel about the program's eligibility requirements and application process, and to run public awareness campaigns each year to recruit employers to hire transitioning service members. The legislation aims to strengthen connections between the military and employers while making the program more accessible to service members preparing to leave active duty.