Is is possible to export a map from ArcMap and import it onto ArcGIS online?
However, once the map is on ArcGIS online I'd still like to be able to edit it so I can continue to update the information if needed.
you can export feature services, which will maintain the symbology and you can activate editing. You will need an organizational account as this is not possible with the free account.
Publish features—ArcGIS Online Help | ArcGIS
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