I’m a returning student and I plan to work in the same department where I worked last year. Do I have to apply again this year?

In most cases the answer is no, but it is up to the supervisor.  Supervisors may require students to re-apply each year, but if not, your supervisor will need to complete a new contract for the upcoming academic year renewing your student employment within their department.   Reach out to your supervisor before the semester starts to let them know you are interested in returning as their student employee for the coming semester (or year).