TL;DR

I searched for other lists of biosecurity newsletters specifically and didn’t find one that suited my needs, so I made one! Please leave a comment with any other newsletters that I missed so that I can add them.  I hope you find something useful in this list. 
[Edit: Added the recommendations from the comments]

Newsletters

1. Johns Hopkins Center for Health Security (CHS) → subscribe here
2. Health Security Headlines (also from CHS) → subscribe here 
3. Center for Infectious Disease Research and Policy (CIDRAP) → subscribe here
4. Global Biodefence → subscribe here
5. Pandora Report → subscribe here
6. Nuclear Threat Initiative (NTI) → subscribe here
7. Bipartisan Commission on Biodefence → subscribe here
8. The Association for Biosafety and Biosecurity (ABSA)→ subscribe here (scroll to the bottom)
9. Council on Strategic Risks (CSR) → subscribe here
10. Biomedical Advanced Research and Development Authority (BARDA) → subscribe here
11. Administration for Strategic Preparedness and Response (ASPR)→ do not recommend subscribing as it is very narrowly biosafety oriented and is sometimes poorly referenced.
12. CBW Events (daily reports from Bioweapons Convention meetings) → subscribe here 
13. The Century of Biology
14. Codon
15. SynBioBeta (@Tessa usually skims this one)
16.  Force of Infection (@Tessa has recently been skimming this one)
17. Something in the air 
18. A list of biosecurity policy recourses is here. 

Comments

I sourced a lot of these from recommendations by Caitlin Walker, as well as from looking through various posts by Chris Bakerlee and Tessa Alexanian. Please don’t hesitate to point out any links that are broken, comment about the relative quality of the above newsletters, or comment with any newsletters that I have missed. Thank you!