Not in JIRA, as JIRA isn't really for that.
But it is in JIRA Service Desk. It's not what I think you are really talking about, but JSD has "Automation" that can do this sort of thing.
There's a rule for Automation that shows as "Keep on top of SLAs" - that should enable you to set up a form of escalation. Have a look at Project Settings - Automation.
Hi Atlassian community, My name is Max and I work on the product integration team at Atlassian. I am pleased to announce the early access program for the Jira Cloud add-in for Outlook. This add-in...
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