This is definitely not an easy question and have multiple questions that needs to be answered before you go ahead and implement it, for example what language are used in the tickets, is their heavily specialized terms used, can specific fields be assigned more weight etc.
You can start by just reviewing the wikipedia sections of NLP (https://en.wikipedia.org/wiki/Natural_language_processing) for some of the issues in regards to semantics and syntax just to get a brief understanding of the issues involved.
As a test you could start by extracting text data from Jira and paste it in one of the many free word analysis tools online like: https://www.online-utility.org/text/analyzer.jsp
That way you can see what your result looks like, most likely the common words such as and/or/want etc the tool you need will now have to understand in your language what words are important and not.
If you are running on cloud i guess you could take a look on this plugin as well https://marketplace.atlassian.com/apps/1219610/knoetical-ticket-analysis?hosting=cloud&tab=overview but i would not get my hopes up for an easy quick fix solution.
Otherwise there are numerous NLP tools out there, its just a matter of finding one that will integrate with Jira and match your requirements in language, terminology extraction, stemming etc.
There are many that will say that they can do it, but the difficulty will be to find one that get a high enough validity in the data that you extract, this is especially so if you plan on automating stuff from the data.
An example lets say you have non english speakers, that want to redo the moving of a folder between systems, and state that they want to re-move it.... whoops boom there goes that folder :-) Silly example but you get the meaning, things are never as easy as you want them when people are involved.
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