Kurt Shintaku's Blog

In case you missed it, yes, Office Professional Plus 2013 client is no longer supported for use with Office 365 services.

This most notably means Outlook 2013 may not function correctly with Exchange Online as of last October 2020. 

Note regarding TLS 1.0/1.1 Support  
Connectivity to Office 365 through Office 2013 may also be related to our deprecation of TLS 1.0/1.1.
https://docs.microsoft.com/en-us/microsoft-365/compliance/tls-1.0-and-1.1-deprecation-for-office-365

(Hopefully this is not new to you as this deprecation of support was announced 3 1/2 years ago via Premier Support newsletters, the Office 365 blog, the Office 365 Message Center for admins and documented in the System Requirements for Office 365)

NEXT STEPS
If you haven’t upgraded from Office 2013, the options are:

1. Update to Office 365 ProPlus
   (Doing this will ensure your organization won’t have to deal with this again in the future)
2. Upgrade to Office Professional Plus 2016 or 2019
   (Moving to 2016/2019 will kick the can down to October 2023 when Office 365 support for these perpetual clients ends – just like 2013 has)

For more details, visit:

• https://techcommunity.microsoft.com/t5/office-365-blog/office-365-system-requirements-changes-for-office-client/ba-p/62327