I am trying to share a map as a service and overwrite an existing Feature Service in ArcGIS Online. I put together a small model to connect to the database, to publish and replace existing item online, but I am not seeing the "Share As a Service" tool in the ArcToolbox. How can I share it as a service with ModelBuilder?
You won't see any option to share as a service from the toolbox itself. In 10.1 the change was made to publish results, which is the information about successfully running a tool. (That can be a system tool, a python script tool or a model tool). Your entry point for creating a geoprocessing service is the Results Window.
See the Quick Tour for more information.