The plugin TestRail for JIRA allows you to see related information in JIRA in regards to these QA testing. However, it does not appear to create custom fields within JIRA's database to store that data. I suspect that since this plugin requires you to connect the JIRA instance to this testrail system, that this data is not within the reach of JIRA to be indexed. And if JIRA can't index this testrail data, you can't search within JIRA for it. So from what I can see about this plugin, I don't think this is possible to do in JIRA at this time.
But of course I would defer to someone from that plugin vendor, Gurock, that would know more about this particular plugin.
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