User created a custom role and the role does not have access to the Global Search bar.
Add the Perform Search permission to the new role you have created in order to have the Global Search field.
Log in as Administrator.
Navigate to Setup > Users/Roles > Manage Roles.
Edit the role.
Under Permissions tab > Lists subtab, add Perform Search and set Level to View. For more information, see Access Levels for Permissions.