This option is available on ArcGIS online, but I have not figured out if this can be acheived on the ArcGIS server.
Slippy map is a very easy way for developers to consume a map service and is widely supported. Your map service layer API on ArcGIS online look something like this:
https://tiles.arcgis.com/awsødkøaslkd/arcgis/rest/services/<service name>/MapServer/tile/{z}/{y}/{x}
Is this possible on ArcGIS Server?
https://wiki.openstreetmap.org/wiki/Slippy_map
Are we talking a standalone server?
With Enterprise, it's a "hosted imagery layer" by name, but under the hood, it's just XYZ tiles.
https://pro.arcgis.com/en/pro-app/latest/help/sharing/overview/publish-hosted-imagery-layers.htm
Personally, I find it easier to generate the XYZ tiles and throw them into a web directory or cloud storage location, that way the tiles can be served at the URL of your choosing.