JSFiddle - React, Tailwind, and code Playground

HTML

<select id="sel">
    <option value="default">Default</option>
</select>
<button id="add">Agregar</button><input type="text" id="opt"><br>
<button id="del">Eliminar</button>

JavaScript

$(function(){
    $('#add').on('click', function(){
        var opt = $('#opt').val();
        $('#sel').prepend('<option value="' + opt + '">' + opt + '</option>');
    });
    
    $('#del').on('click', function(){
        $('#sel option:selected').remove();
    });
});