Not really. I'm not aware of any addons that do any form of integration, but I know a number of people have written some simple stuff (Jira has email, SOAP and REST interfaces - I've seen email and SOAP used ini the past, but would expect more recent stuff to move to REST because SOAP is deprecated).
However, you need to start by defining what you mean by "integrate"? It's quite difficult when you're working with legacy systems like Remedy as they can be quite insular and not expose much in the way of useful automated interaction.
The last three places I visited with a remit of "how do we integrate with Remedy" quickly decided that moving off Remedy on to something with better functionality (no, not always Jira) would be a better investment than trying to bludgeon Remedy into being useful.
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