How to run xpath on element

We all know that we can run execute xpath expression in console on the DOM element.

I wanted to know if we can to the same against an element.

lets say

elem = $x("//li[@class='myclass' and .//a[text()='text_in_elem']])

Now I want to execute a new xpath expression on elem.

Is it possible like we can do multiple chains of .querySelector()

Thanks.