After installation of Elastic Search extension the search in my site gives no results.

It is required to make sure that all the necessary configurations were made.

First of all,  please check what search engine is selected for your site in default Magento settings.

Go to Stores > Configuration > Catalog > Catalog > Catalog Search and check what option is set in the Search Engine field:

Then, check the connection with the engine. For this, go to Stores > Configuration > Elastic Search > Connection:

Then, click the Test Connection button and make sure that you see the "Successful! Test again?" message.

Moving on with the version of the Elastic Search engine installed on the server. At the moment, the module supports versions from 6.x up to 7.6. To check the currently installed version, please run curl - XGET localhost:9200 (where localhost is the Elasticsearch Server Hostname and 9200 is Elasticsearch Server Port).

After setting Amasty Elasticsearch as a Search Engine, checking the connection, and saving the settings, please make sure to run reindex from CLI.

If all of the above is configured correctly and your search is still not producing results, please create a support ticket with us as your site may conflict with a third-party extension.