Awareness Nurture Series Lead Acquisition

Hello marketers! I'm new to my role and my company currently has a Welcome Email set up for those who sign up for our emails on our website. I'm in the process of building an awareness engagement program to stick new leads in.

What's the best way to get people who sign up for our emails and receive a Welcome Email, into the new Nurture/Awareness stream?

Thank you!

Seen above - NUR-Welcome is the existing program that sends a Welcome Email to new leads who sign up.
NUR-Awareness is the program that I need to get these leads ​into​.