@Laurenventure I don't connect to City Works, but I have created Read only feature services, within the ArcGIS Enterprise environment, for consumption in older applications like ArcMap.
The key thing is to curate the services as not editable, and not load your actual network in the service. In my current example, I have just my network lines loaded into my ArcGIS Pro Map, publish to ArcGIS Enterprise, and that service which I created I can load into ArcMap.
Hope that helps.
Brian Colson, GISP