Other providers like you answer online questions (f.ex. Quora), maintain blogs, participate in online fora (Linkedin, etc.) with the purpose of increasing visibility of their newsletter offering. Not in a "subscribe to my newsletter"-message, but just honest Q&A with a link to their newsletter in their bio.

Just promoted a seminar on Linkedin from my company page, and it gave 30 new followers of our company. Not subscriptions, mind you, but visibility must be key here, linking to a landing page, where you explain the value you create - perhaps with testimonials from your trusted subscribers.

Good luck!