First, you will want to replace this employee's schedule with Unassigned so that you can preserve the pattern for the person who is hired as a replacement. You can do this with the Pattern tool by clicking on the first day that they no longer work for you and then replacing their schedule with Unassigned.

Then, you will need to archive this employee's profile in the people page. To archive an employee's profile, go to the People page at the top of the screen.

Search for the employee's name who no longer works for you. Click the Edit button once you find their profile.
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Scroll down to the bottom of their profile and click the red button that says "Archive Employee" to remove them from your active list of employees.
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Once an employee has been archived, you can find their old profile by clicking on the three dots next to Add Employee and then selecting View Archive. If you ever need to add them back to your facility, simply click Unarchive.