Is there a way in elastic search to trigger an alert or the entire document, whenever INSERT/UPDATE is performed on the document?
No, Elasticsearch does not have any concept similar to RDBMS triggers that I am aware of.
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The only way I could think to do this would be to monitor Elasticsearch's HTTP port (9200) using Packetbeat, and then filter out everything except those two actions. Then save that output to Elasticsearch and setup an alert on that.