Create a Segregated Document Library in SharePoint
If you are an owner of a Team site in SharePoint, you may wish to create document storage with specific permissions which are separate to the default document library.
Create a Document Library
From your SharePoint Home Page, click the Settings cog and select Site contents
This takes you to what is effectively the root directory of a SharePoint site folder structure. use the + New button to select Document Library
For most requirements, create a Blank library and deselect the Show in site navigation box. The navigation box is configurable so unless it’s an important library that needs to be accessed by everyone from any page on the SharePoint site, there is no need to have it in the navigation. [You can also add a quick link button anywhere on your Home Page if it’s frequently use.]. Sensitivity labels seem to only be configurable at tenancy level.
Once you’ve created your library, you can configure permissions from the Library settings > More library settings
Select Permissions for this document library
The standard permissions are inherited from the site. The default options for a new library are Manage Parent, Stop Inheriting, or Check [a user of group]. In order to make permissions different to the top-level site permissions, you need to stop inheriting permissions
You then have more options, and can select an existing group or Grant permissions to a new user or group
As an example, the Members group has been reduced to Read only, and the IT Services team can be added. You can add any Office365 group (ask your IT team) if you know it. It could be members of a linked group in the tenancy, or people who have access to a shared mailbox.
You can change what you share with these users or groups. The SHOW OPTIONS allows further customisation.
Unchecking Send an email invitation is useful when using large groups where not everyone requires immediate access. Then you can specify which level of permissions you are granting.