Zendesk provides a very nice JIRA integration widget that allows creating JIRA cases directly from Zendesk and keeps them in sync.
The widget however is missing some features. It only supports setting values for certain fields on the JIRA ticket. In our case this was a problem, since for certain issue types we have priority as mandatory field. Therefore I created a new version of the widget, which supports also priorities.
The widget is available on github: https://github.com/juhap/zendesk-jira