You can use the Azure DevOps Services REST API to export the work item type definition from the source organization. You can retrieve the XML definition of the work item type by using API calls.
Once you have the XML file, you may need to edit it to make sure that it aligns with the requirements or customizations in the target organization.
Then, import the edited XML definition into the target organization using the Azure DevOps Services REST API. This will create a new work item type in the destination organization based on your template.
If you want to use some tools, you have Azure DevOps Migration Tools, which can help automate the process of migrating work items, including templates, between organizations.