I believe you're trying to use Trello with JIRA or another Atlassian product, is that correct?
If so, the Power Up is part of Trello itself, not of JIRA. That is, you get the JIRA integration within Trello but not the other way around.
Here's some installation instructions for the Power Up: http://help.trello.com/article/1081-using-the-jira-power-up
I'm not aware of any official Trello add-on for JIRA itself, although there's some 3rd party synchronization tools in the Atlassian Marketplace: https://marketplace.atlassian.com/search?query=trello
Trello's API outputs in XML. From there, I figure minimal dev effort could produce a simple middleware that PUTs Trello data into JIRA.
An ESB like Mulesoft could be used as a platform to translate and transport that data. No point in reinventing the wheel ;)