TLDR: No. But not because of ES6.
ES6 is a new version of the Javascript language. It has a lot of new syntactic sugar on top of plain old Javascript and it does, of course, improve developer productivity leveraging modules, a decent OOP-like syntax and a few other tricks.
jQuery on the other side is a library that helps with DOM manipulation.
The DOM is the virtual representation of a web page for your JS code. The standard DOM API are provided by the browser, and you can think of it as a "plugin" for JS to HTML nodes.
The problem has always been that the DOM API is terrible. Like so terrible that you don't ever want to use it directly. And each browser did things in a different way.
jQuery solved all of this by providing a lean interface to the DOM API, which is, by the way, uniform through all browsers. Bingo!
ES6 does not change in any way how you access the DOM. It only changes the language core.
So, "why you wouldn't use it then?" you may ask.
TLDR: CSS3 and React/Angular
90% of what I did with jQuery were animations and magic tricks on particular events. Now, if you have a deep knowledge of CSS, you don't need JS at all for this kind of stuff. _CSS Transitions, animations and transformations to the rescue. _They are faster, work well across many browsers and do not require scripting.
What remains of the jQuery use cases is today completely overridden by a proper Frontend engine like React or Angular (I do prefer React). Let them take care of the DOM.