Trying to start the bitbucket server, but throwing an error stating "BIND TRANSPORT EXCEPTION"

I don't know the tools you are using. 7993 is not a standard port for elasticsearch.

Can i change port ?

In elasticsearch, yes with transport.port: 9300 and http.port: 9200. But is it your question?

Is there any standard procedure to overcome the current issue and kill running port ?

It depends on how you started elasticsearch. If you did that manually on the command line, then a CTRL+C would work.
If you started it as a service, stop the service...
Or kill the process.