I have a default installation of Elasticsearch which I am trying to query from a third party server. However, it seems that by default this is blocked. 
Is anyone please able to tell me how I can configure Elasticsearch so that I can query it from a different server?
There is no restriction by default, ElasticSearch expose a standard HTTP API on the port 9200.
From your third party server, are you able to: curl http://es_hostname:9200/?
Allowing remote access to Elasticsearch