Based on your stated requirement of "standalone management for the team", I suspect what you will need to do to fulfill that request is to
1- Make an ENTIRELY NEW Primary Site, new site code, new server(s). Carefully define the boundaries.
2- Reinstall all the clients which should report to that new primary site with the addition of the RESETKEYINFORMATION=TRUE parameter so those clients begin reporting to the new site.
Note... I suspect you are going to have a lot more issues than you might expect, due to boundaries and possible automatic site code assignments. It's not fun to do this.
Alternative: what is the actual business driver requiring that a particular team have their own 'primary site'? Are you and they certain that the business requirements cannot be fulfilled instead by properly setting up Role Based Access, and properly defining the collection(s) that team can see, and other objects that team can see from the CAS level? To me, that is one of the main methods of carving out rights so that Team A can only see the things Team A is responsible for, and Team B cannot see Team A's stuff.