When creating a new label for an ArcGIS Server map service published from ArcMap in ArcGIS Online Map Viewer, there is no option to add a new expression.
This is a known limitation. ArcMap does not support Arcade expressions. Therefore, map services published from ArcMap do not have the option to add Arcade expressions for labeling.
Solution or Workaround
Choose one of the following options to circumvent this issue:
Publish the map service from ArcGIS Pro
A map service published from ArcGIS Pro to ArcGIS Server allows labels to be created with Arcade expressions in ArcGIS Online. Map services can be published from ArcGIS Pro to ArcGIS Server through federated servers. For more information on publishing a map service through federated servers, see Portal for ArcGIS: Layers published to your portal's federated servers.
Add an individual layer from the map service
Instead of adding the map service to Map Viewer, add an individual layer from the map service. This allows a label to be created with an Arcade expression on the layer that is added. For more information on adding a layer from a map service, see ArcGIS Online: Add layers