It looks like this is an Airtable interface.  If that's correct and you go into edit mode highlight the link to bring up the edit panel on the right.  You should see a "Perrmissions" section at the bottom.  Toggle the selection to allow the user to create new records and you should be ready to go.  

Thank you for your reply. But I don't see it =(

I'm having the same/similar issue. I have a Customers form and I want them to be able to add their pets. When I click +Add under Pets, I just get a list of currently entered pets. How can I actually add one? Thank you.

It seems that now there is no such functionality 😞 I searched all over and did not find anything 😞

Hi there!

At miniExtensions, we've created a third-party form designed exclusively to integrate with Airtable, giving you full control over users’ ability to create or expand records in linked tables. You can combine this with other useful features, such as using different forms for creating and expanding records, prefilling child forms when creating records, and customizing the title of the “create records” button, to name a few.