If so, how do you announce it in a newsletter without it looking like spam to them?
If your new thing would be of value to your subscribers - then sure.
Let them know "WIIFM?" in language that makes sense to THEM (in other words - use good marketing).
Assuming the product/service + the message + the offer is a good fit it won't be considered spam. Give them a chance and a good reason to opt in to a new list for your new project. And remember to monitor your stats (open rates and CTR).
Let me know if I can help in any way.
Best of luck on your new venture!