Click on "field settings" in the top right hand corner of that screen. That's where storage specific options are held.
If you can edit the options there then it's a simple text list. But it may be that field is referencing a taxonomy term or content/entity but that tab will lead you in the right direction to add an item
Once a field is created, you can still change its settings clicking on the Field settings tab you see in the screenshot you took.
As you notice, the warning tell you the settings cannot be longer changed, as there is already a node containing data for that field. That doesn't mean you cannot change anything for that field. For example, I was able to add a new value to the list, which is what you want to do.
What you cannot do is removing values that are used. In that case, you get an error message, similarly to what happened to me when I tried to remove the default value (frontpage|Front page), which was used from the test node I created.
The message is clear: Allowed values list: some values are being removed while currently in use.