You will need to find or write code to do that (I'd do it in the script-runner add-on)
The most simple solution is a post-function added to the transition(s) that should trigger the change on a linked issue. It will need to read over all the links, check the current status of the issues at the other end of the link, and then push them through the appropriate transitions if they need it.
As a Jira power user, I was at first doubtful that Trello could benefit my workflow. Jira already uses boards (ones you can customize!), so why would I even need to use Trello?! In this post you will...
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