I want to publish a service.
You will have to contact your Organization account administrator and ask them to add you as a publisher in the AGOL account. You can also check with your colleagues if they are already added to the organization account.
Once the account is available you should be able to publish the services.
Meanwhile you can refer the following links:
Create account—ArcGIS Online Help | ArcGIS
Join organization—ArcGIS Online Help | ArcGIS
Publish hosted feature layers—ArcGIS Online Help | ArcGIS
I hope this helps!
In case you don't have an ArcGIS Organizational Account, and you require it for self learning purpose (and you are not sure of getting an ArcGIS Online subscription), you could checkout the ArcGIS Trial (21 Days) or signup for the ArcGIS Developers Program.
Many thanks for yer comments. I have now solved the problem. I was signed into our ESRI organisation account, not our ArcGIS Online organisation account.
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