It is not possible to move a TSS from one (managed-)organization to another.
As each (managed-)organization is technically a different location, a TSS should always be assigned to a certain location.
Tip: In case a TSS is no longer used in an organization, it is recommended to disable the TSS and also de-register any clients connected to it. However, please be aware that once a TSS has been disabled it is no longer possible to deregister a client - see SIGN DE - Can I deregister a client once a TSS is disabled?