JSFiddle - React, Tailwind, and code Playground

HTML

<table>
    <tr>
      <td>
        Tytuł
      </td>
    </tr>
    <tr>
        <td>Rekord jeden</td>
        <td>
            <a href="#" class="up">Up</a>
            <a href="#" class="down">Down</a>
        </td>
    </tr>
    <tr>
        <td>Rekord dwa</td>
        <td>
            <a href="#" class="up">Up</a>
            <a href="#" class="down">Down</a>
        </td>
    </tr>
    <tr>
        <td>Rekord trzy</td>
        <td>
            <a href="#" class="up">Up</a>
            <a href="#" class="down">Down</a>
        </td>
    </tr>
    <tr>
        <td>Rekord cztery</td>
        <td>
            <a href="#" class="up">Up</a>
            <a href="#" class="down">Down</a>
        </td>
    </tr>
    <tr>
        <td>Rekord pięć</td>
        <td>
            <a href="#" class="up">Up</a>
            <a href="#" class="down">Down</a>
        </td>
    </tr>
</table>

JavaScript

$(document).ready(function(){
    $(".up,.down").click(function(){
        var row = $(this).parents("tr:first");
        if ($(this).is(".up")) {
            row.insertBefore(row.prev());
        } else {
            row.insertAfter(row.next());
        }
    });
});