If you have a Microsoft 365 subscription, you should not see ads in your message list in new Outlook or the message list and banner ads on the right in Outlook on the web.
The rules for new Outlook are basically the same as for Outlook on the web: the account needs a subscription to go ad-free. The only difference with new Outlook is the account with the subscription needs to be the primary account and all accounts will be ad-free in new Outlook. Business accounts without Microsoft 365 software licenses can be added to new Outlook as long as the primary account has a subscription.
To set an account with a Microsoft 365 software license as the primary account in new Outlook at View tab > View settings > Accounts. Click Manage button next to the account with the Microsoft 365 subscription and Set as primary account.
If the Microsoft account address for your subscription is a third-party address aka EASI (Email As Sign In), at this time new Outlook will show ads. Microsoft is working on a solution so users with EASI addresses can sign into new Outlook to remove ads.
Until then you would need to add an outlook.com alias to the Microsoft account and add the account to new Outlook as the primary account. If you don't want to use an alias, turn on Focused Inbox. The Focused tab will be ad-free while the Other tab will have 2 message list ads at the top.
Ad example when Focused Inbox is not enabled:
Ad example when Focused Inbox is enabled, with 2 ads on the Other tab (although not shown, there are no ads on the Focused tab.)
More Information
About ads in Outlook (Microsoft support)
