Hi,
It would be nice to have a more detailed post of what you are asking, but I will attempt to guess...
If you are referring to changing the symbology on a publishing level (not a user having the ability to change the symoboloy)
Symbology can be changed on the Web Map level.
Left click on the layer in the web Map >> Change Style
Ref:
Change style—ArcGIS Online Help | ArcGIS