This Esri document also lists which clients require update/fixes to support TLS 1.2, including what Esri products and a list of older browsers.
Esri has also established a support page to help customers at https://support.esri.com/en/tls.
How will this affect Nearmap users?
When you try add a layer from ArcGIS Online, and your application hasn't been updated, you may get an error similar to this one:
To fix this connecting to ArcGIS Online via ArcMap:
You may encounter the following error:
To fix this you will need to update your software with the patch as described in: Install the TLS 1.2 patch on ArcGIS Desktop.