I think you are after a secondary navigation.
Head to Appearance > Menus and create a new menu with the some custom links (contact, phone # etc) you want, then click the “Manage Locations” tab and assign the newly created menu to “Secondary Menu”.
Then you can position it above header in Customizer > Layout > Secondary Navigation > Navigation Position.
Additional customization available: https://generatepress.com/knowledgebase/generate-secondary-nav/