There is not something like a connector available to link JIRA to Remedy. You could however make use of mail handlers and notification messages on events in both systems to transmit information back and forth.
For JIRA mail handler configuration, here.
For JIRA mail notifcation configuration, go here.
For JIRA custom events, go here.
For the configurations on Remedy side, you will have to check with your Remedy supporter.
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