If you do not use Advanced Planning in Jira Cloud, you can utilise Issue Links to connect the issues above Epics and below Stories to each other. The Stories can be linked to Epics using the Parent field.
If you are connecting to a self-hosetd Jira or not sure how the issue hierarchy in your Jira is set up, start here.
The below example will work for the Initiative > Epic > Story > Task (Bug) > Sub-task hierarchy.
Use Parent mapping to link Stories to Epics and Sub-tasks to tasks:
Use Issue Links to connect everything else, including Epics to Initiatives. You will need to create a new link type as there is no suitable link type in a new Jira instance. In the below example, we have created a link type Hierarchy. It WILL NOT EXIST in your Jira. You will need to create it.
If you copy information only from JIRA to MS Project and do not need to update Parent and Issue Links in Jira, you can disable the issue type filters.
To copy the hierarchy from MS Project to Jira, the filters must be configured as shown above. Also, you will need to map Issue Type to a custom text field and populate this field with the issue type for each task that is associated with an issue of a non-default issue type:
That will ensure that the issue type filters in the Parent and Issue Link mappings above work correctly.
To create multiple issue types, e.g., Epics, Stories, Sub-tasks in Jira, you will need to map issue type and populate the mapped column, anyway.
If you are importing issues, map Issue Type as described above, and the issue type will be copied from Jira.