To add a field to your existing feature service in AGOL, follow these steps.
1. Locate the layer in your content (you need to be the owner/publisher, I believe)
2. View the item details
3. Select the Data tab
4. Switch from Data to Fields on the selector at the top
5. Choose "Add Field"
6. Configure the field as desired
7. Save
EDIT: Please note, if you have a view layer (e.g. a stakeholder viewing layer) set up, you will need to add the field to the source. If the view layer does not automatically update after a few minutes, you may need to add the same field to the view layer.