Jira does not allow to show third-party elements on the Issue Create and Transition screens but you can work-around it and show Checklist Text custom field.
When the Checklist Text custom field is present on the Create/Transition screen, you can add checklist content in the text format and get and the final checklist on the Issue View page.
Note that:
The Save local checklist items to Jira custom fields global setting must be enabled.
As an alternative to adding the Checklist in text format on the Creation screen, you can set a template to automatically be added when issues of a given type are created in a project.
If you show the Checklist Text custom field on a transition screen and want to block the transition depending on the field value, you will need to use a Regular Expression validator. The built-in validators will not work in this case because of the order of operations.
Adding the Checklist Text field to create and transition screens can only be done in Company-managed/Classic projects
Adding a Field to a Screen
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When filling out the Checklist text field, the checklist must be properly formatted. The easiest way to do this is to prepare the checklist on an existing issue and then copy it from the checklist editor.