You can do both:
- If a plugin exists for JIRA integration or accessing data from JIRA, and it does what you need, then yes you can use it
- If it does not, or you prefer to build your own, that too is an option
However, I cannot recommend a particular plugin, and you will need to consult JIRA API documentation for details on how to build your own.
You can use the
WP_HTTP APIs to speak to the JIRA API, though you will need to ask in JIRA developer communities for how to speak with those APIs to retrieve the data you desire.
Once you have the data, you can store it and display it on the frontend using various options:
- page templates
- posts created using the data that was retrieved