A best practice post-GDPR is to add a snippet in your privacy policy for each service you use that has access to your customers' personal data like names and email addresses.

You can add the text below into your privacy policy:

We use the email distribution service provided by SmartrMail Pty Ltd based in Australia (https://www.smartrmail.com). SmartrMail assists us in creating, scheduling, and delivering our newsletters. SmartrMail acts as our data processor and it may have access to your name, email address, IP address, and cookie-related data, which is necessary for newsletter delivery and analytics purposes. To make sure that your personal information is properly protected, we have concluded a data processing agreement with SmartrMail that ensures the highest level of protection for your personal information.
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If you would like to know more about SmartrMail data protection policies, please refer to their privacy policy.