Office 365 (Outlook 2016) - Hyperlinks Failing when Clicked
When Internet Explorer is set as the user's default browser in Windows, clicking on a hyperlink results in one of two errors, depending on user's version of Outlook.

In order to correct the issue, Internet Explorer settings will need to be reset for your specific version of Internet Explorer (IE):
2. Select Tools > Internet Options.
3. Select Advanced > Reset.
How to Reset Internet Explorer Settings in Internet Explorer 11 and Internet Explorer 10
1. Start Internet Explorer.2. Select Tools > Internet Options.
3. Select Advanced > Reset.

4. In the Reset Internet Explorer Settings window, select Delete personal settings > Reset.

5. Select Close when this has completed.

6. Close and restart Internet Explorer
7. Select Tools > Internet Options
8. Select Programs > Set programs

9. Select Set Your Default Programs

10. In the Programs list, select Microsoft Outlook > Set this program as default.

11. Scroll back up to the top of the default programs list and highlight Internet Explorer and select Set this program as default.

12. Select OK and close the Default Programs box.
1. Start Internet Explorer.
2. Select Tools > Internet Options.
3. Select Advanced > Reset.
3. Select Advanced > Reset.

4. In the Reset Internet Explorer Settings window, select the Delete personal settings > Reset.

5. Select Close when it is completed.

6. Close and restart Internet Explorer
7. Select Tools > Internet Options
8. Select Programs > Set programs

9. Select Set your Default Programs

10. In the Programs list, select Microsoft Outlook > Set this program as default.
11. Select OK, and then close the Default Programs dialog box.
12. In the Internet Options dialog box, select the Programs tab, and then click Make default under Default web browser.

Advanced Settings
For the more experienced, tech savvy computer user, the below link provides additional information.
How to Fix Failing Hyperlinks in Microsoft Outlook