When you no longer want a job to be displayed to students, you can set the status of that job to cancelled.
Cancelled jobs do not show up to students, and are only visible to you.
Alternatively, you can use the old job that you wish to delete as a template for when you want to create and add in a new job. Simply edit the job, and add in all new information before setting the job's status back to pending.
If you really just need the job deleted and gone from all views, including your own, Purple Briefcase can delete them for you.