By default, ZERO "subscribes" all users to all new posts. This means all team members will be notified about new posts that are created in the Team and all subsequent activity on the post (assuming all users remain subscribed to the post once the post has been created).
If you are an Admin or Team Lead, you have the ability to turn OFF this team-level notification setting. You can do this by editing your Team Settings. When you uncheck this box, all users in this Team will no longer be automatically "subscribed" to new Posts going forward.
For more on how Subscribers/Notifications work in ZERO, click here.
Click on the gear icon in the upper right corner of your screen and select Manage Teams:
Click on the ellipsis next to the team that you want to update and select Edit team settings:
Then uncheck the box next to Subscribe all team members to new posts.
Be sure to select "Save Changes" before navigating away from the dialog box.