Hello Ian and welcome to the Community.
Out of the box, the integration won’t trigger on a not responded within a timeframe. There is hope though, you may create webhooks and with the help of automation scripts or apps you can have something check your issues for response time and update the ticket as not reponded or needing update. From this update you can have the slack integration trigger a webhook that sends an update when an issue has been updated to not responded.
Depending on the product you’re using you will need to review the API to find and update your issues. You may also apply a JQL statement with REST API calls to find the issues which have not been updated. I would review the following REST API endpints:
I hope this proves helpful and you’re able to create automation to trigger alerts when issues need to be responded to.
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