How can I ensure that a change that spans multiple repositories is deployed synchronously?

[Jonathan Needham]

I have many repos which have changes that will require other services/API endpoints to be in place to work fully at the system level (microservices architecture). How, in Jira, can I ensure that I don't end up deploying a half fixed system. Realistically, I want something like a deploy-on-epic completion interaction with the CI where only when a particular epic is complete can all changes contributing to that epic be deployed to live.

Anyone have any ideas/solutions etc? Of course, there is a chance that there is a fundamentally simpler solution to this and I may have already got stuff wrong.

Thanks