Atlassian do not support the addons you need to do this in full, and it doesn't look like this is on the roadmap to add to Cloud any time soon. So the best you'll be able to do is code for Teamcity so that it can use JIRA's REST interface to read and update JIRA.
I’m a designer on the Jira team. For a long time, I’ve fielded questions from other designers about how they should be using Jira Software with their design team. I’ve also heard feedback from other ...
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
You're one step closer to meeting fellow Atlassian users at your local meet up. Learn more about AUGs