You will Receive alerts for new activity via email if this option has been set on the related service settings.
To change this, please go to Services > My services, select the service you are getting the alerts for and click on it to access the settings for that service.
In your service settings change the alerts to be sent to your Priority Inbox Only. This way you will still be able to see any new activity within Sendible by going to Engage > Priority inbox, but you will stop receiving these alerts via email.
Alternatively, if you do not wish to receive any alerts, in your Priority Inbox or via email, select None.
Make sure to select the Save Changes button once you've adjusted this setting.
You may still receive a few alerts via email once you've changed the settings if these have already been queued before the setting was changed. Once these are sent to you, all email notifications for that service will stop.