I see you have purchase the Extension Pro Pack, thanks!
You can use the Form addon to add a form where your site visitors can submit entries to the directory.
Here’s the instructions for how to setup Form:
Since you used the work “registration”…
If your intent is so your users can add and maintain their own entry, you need to setup the Link addon. Here’s the link to the docs:
You should not enable the Submit Entry link for this use case. For WordPress user registration, you can use the core WordPress registration features which are built into WordPress. Or, alternatively, you can use any plugin that enhances those features. Connections does does not have this built in since there are many great/freely available solutions to process user registrations. After the WP User has registered, they will then be able to add and maintain their entry in the directory.
I hope this thoroughly answers your question. Let me know.