Yes, you can connect Trello to Jira. There are a few different ways to do this, depending on which tools you're using.
If you're using the Atlassian suite of tools (Jira, Confluence, etc.), you can install the free Trello for Jira app. This app lets you create boards and cards directly from Jira issues, and gives you a number of other features specifically for integrating Trello and Jira.
If you're not using the Atlassian suite, you can still connect Trello and Jira using the power of the Zapier platform. Zapier lets you create "zaps" that watch for triggers in one app and take actions in another. So, for example, you could create a zap that watches for new issues in Jira and creates corresponding cards in Trello. Or, you could create a zap that watches for new cards in Trello and creates corresponding issues in Jira.
There are a number of other ways to connect Trello and Jira, depending on your specific needs. For more information, you can check out this article: [Insert Article].