In new navigation, UI doesn't show the "App navigator" custom links section unlike in Old navigation.
Screenshot attached for New Navigation and Old Navigation respectively.

Actual experience

1. Click on the Atlassian switcher menu (the nine-grid icon in the top left part of the nav)
2. Custom links set from the Application navigator are not shown

Expected experience

1. Click on the Atlassian switcher menu (the nine-grid icon in the top left part of the nav)
2. Custom links from the Application navigator will appear at the bottom of the menu
3. Site admins should see a "Manage list" button at the bottom of the menu