JSFiddle - React, Tailwind, and code Playground

HTML

<div class="select_main">
<p></p>
<select>
    <option>Значение</option>
    <option>1</option>
    <option>2</option>
    <option>3</option>
    <option>4</option>
    <option>5</option>
    <option>6</option>
</select>
</div>

CSS

.select_main{
width: 140px; 
height: 18px;
margin: 0px 5px;
position:relative; 
color:black;
display: inline-block;
border: 1px solid #C8B5A1;
font-size:13px;
}
select {
width: 140px; 
/* height: 20px; */ 
position:relative; 
border:none; 
cursor: default; 

color:black;
}
.select_main p {
height:100%; 
position:absolute; 
top: 0px; 
color:#0a0a0a;  
line-height: 18px; 
overflow:hidden;
}

JavaScript

$('select').each(function(){
	$(this).siblings('p').text( $(this).children('option:selected').text() );
});
$('select').change(function(){
	$(this).siblings('p').text( $(this).children('option:selected').text() );
});