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.