First sign up for an Office 365 Developer Site. Be sure you have access to an Office 365 Developer Site. Here are three ways to get one:
Please refer
Set up a development environment for SharePoint Add-ins on Office 365 for more details.
Content Type Hub
Content Type Hub was introduced in SharePoint 2010 for publishing and subscribing content types. Please refer to the following eBook for more details:
Getting Started with Managed Metadata Service in SharePoint 2010. This works a little differently in SharePoint 2013 Online compared to SharePoint 2010/2013 on premise. Content Type Hub is automatically configured in SharePoint 2013 Online and is hidden in the admin page. Please refer to my
previous article to get the content type hub URL in SharePoint 2013 Online. In this article you will see how to publish a content type from a content type hub in SharePoint 2013 Online.
Publish a content type
I have created a custom content type named “Custom Content Type” in the
content type hub.
Click on the custom content type that must be published. Click on the
Manage publishing for this content type link.
Select
Publish and then click the OK button. The content type is successfully published in the content type hub URL.
Note: It might take some time for subscribing this content type in the other site collections.
Summary
Thus in this article you saw how to publish a content type in SharePoint 2013 Online.