Before ArcGIS Enterprise Sites 10.8, any members who needed to customize and administer sites were added to the Sites Administration Group. This group gave members access to edit any site created in the portal. Now, new and existing sites will have their own core team, giving site administrators greater control of who can edit the site.
The core team for existing sites will include all members of the Sites Administration Group. You can remove members or clone a site to get started with a fresh core team and set your old your site to private or delete it.
To add someone to a core team, open your site in edit mode and click the second dropdown menu in the edit navigation bar and choose Teams. Then, click the Add Members button on the side panel and select your team members.
As a core team member, a person can edit the site and any items shared to the site’s core team group.
To check What's new for ArcGIS Enterprise Sites at 10.8 go through this blog.