We currently do not have this functionality, however, you can reach out to Support to submit a feature request. In the meantime, you can trigger a new incident for the Service from the + New Incident on the Incidents page.
Additionally, if you’re using the (now) default Service configuration of “Alerts + Incidents” you may be able to move the Alert to a new Incident (or the Incident you just created manually), if the Alert itself has not been resolved.
If you’re using an alert submission system which will periodically send updates as Triggers (e.g. Nagios, Sensu), it’s entirely likely a new Incident will be created for this Alert (timeframe depends on your source configuration, amongst other things).