I need to Link the User Story to Test case and Defects, in a such a way that system/Jira should not allow me to change completed status for user story when the Test case or Defect is in-progress status.
You can link the stories in Jira to defects, and bugs. In order to make sure that you can't complete the stories unless the defect or bug is done then you will have to write a validation check in the story workflow which will check for the status of the linked issue.
Paid plugins like JSU and Script Runner can achieve this.
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