I apologize for my late response and thank you for all of your patience while waiting for a reply. I definitely understand how frustrating your situation must be, and I wanted to make sure that your concern was acknowledged. You will definitely need a Nest Connect as @S3bryan said, to make your system work.
Thanks for visiting the Google Nest Community.
Since this thread hasn't had activity in a while, we're going to close it to keep content fresh.
Check out this link for a complete guide for your Nest X Yale lock.
If you have additional questions, feel free to submit another post and provide as many details as possible so that others can lend a hand.
Hope this helps!