Click on Settings and then the Sections tab.  Click on the section link.

Click Edit Section on the right, check the Students can only participate in the course between these dates option, and click Update Section.  This will ensure that the other students will not be able to access the course.

Type in a name for the new section such as Extended Access and click the blue + Section button. Click into the new section.

Click Edit Section on the right, enter the new End Date and click the blue Update Section button.

Click back to the Course Details tab. Scroll down to adjust the overall course End Date and select the Restrict students from viewing course after course end date option. Scroll farther down and click the blue Update Course Details button.

Click on People from the course menu. Click on the options menu (three dots) to the right of the appropriate student and select Edit Section.

Start to type in the new section's name or click browse to select it. The new section will be displayed along with the original section.  Click the blue Update button.

A confirmation message will be displayed in green and both sections will be listed for the student.

Below on the left is what a student only in the original section sees, while the right displays what the student in the new section can access.