Apologies I am a little trouble understanding what exact you need help with. I see you have purchase the Circled template and the Form and Link extensions. These will allow you to take user submitted entries and allow the submitor to maintain their own entry. If you need help with configuration to achieve this, I certainly can help. I am just no certain what you mean by “current users can introduce next level of users to the directory so that the hierarchy“.
Since you would like users to be able to add and maintain their own entries, the first step would be to setup a user registration process. This comes built in to WordPress and many users already have a user registration process setup using third party plugins so Connections does not provide this functionality.
If you do not have this setup, you could use the features built into WP or use a plugin like User Registration. There a many freely available plugins like this you just and to choose one that provide the features you require.
After you have user registration setup, then follow the setup instructions for both Form and link:
- Form: https://connections-pro.com/documentation/form/#Add_the_Submit_Entry_Link
- Link: https://connections-pro.com/documentation/link/#Configuration
If you have not configured Form at all, then you actually only need to follow the configuration instructions for Link.
I hope this helps to get you start. Let me know if you need any further assistance.