JSFiddle - React, Tailwind, and code Playground

HTML

<select id="combobox">
    <option value="">Select one...</option>
    <option value="Apple">Apple</option>
    <option value="Banana">Banana</option>
    <option value="Pears">Pears</option>
</select>
<br />
add value to enter to the select:
<input id="txt" />

JavaScript

$('#txt').change(function() {
    var value = this.value;
    
    var isExist = !!$('#combobox option').filter(function() {
        return $(this).attr('value').toLowerCase() === value.toLowerCase();
    }).length;

    if (!isExist) {
        console.log(this.value + ' is a new value!');
        $('<option>').val(this.value).text(this.value).appendTo($('#combobox'));
    }
});