Hi there!
Jetpack doesn’t allow you to import subscribers from a third-party service at the moment.
Did your old site have Jetpack as well, or was on WordPress.com? In that case, I might check whether I can move the subscribers over as explained here:
https://en.support.wordpress.com/moving-a-blog/moving-your-subscribers/
If the mailing list comes from elsewhere, though, I’m afraid that’s not possible.
I’m reporting your input in here, just to make sure your request gets the right attention:
https://github.com/Automattic/jetpack/issues/535
You’re welcome to follow the thread along to getn otified in case the request gets implemented.
Hope that answers your questions! Please let me know if you have any further questions or doubts, and we’re happy to assist you.