Or, if you're using Postman, it could look like this:
If you do not specify a name field in this create call, the API will return the existing link with the existing name. If you do provide a "name" field, the existing link will be returned, and the name will be updated on the link.
After making this first API call to create or fetch the link, you can issue a call to the list link conversations API endpoint to return all conversations currently tagged with that Link.
I recognize that while this approach should work, it could perhaps be more effective to offer a specific endpoint for fetching Links by their external_url value. This has been previously requested, and I'll go ahead and your vote as a plus one to that feature request to see if this is something we can introduce in the future.
Let me know if you have any other questions or concerns, and enjoy the rest of your day!