Hi @Rory Aptekar ,
I had the same issue,I used Project Automation (Automation for Jira) to send Email to approvers.
If mail subjects contain Issue-Key, replies on them, could be recieved as a comment on Issue.(remember that those comments are added by a Unique/Default user, for example Jira Admin)
You also need to add incoming mail handler. Documentation is here:
Then with another trigger on Project Automation, issue is transitioned and approved when the comment contains specific word. (e.g. "Approved" )
You can add condition to automation using JQL,
and to search for comments containing words or added by someone with JQL, you'll need ScriptRunner plugin.
So it is a little complicated but could be done by adding one or two plugins.
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