JSFiddle - React, Tailwind, and code Playground

HTML

<div style="height:px;" class="roleSelector span-4 prepend-7 last " id="roleSelectorObj"><select><option value="[Markets].[EMEA]">EMEA</option><option value="[Markets].[NA]">NA</option></select></div>

CSS

div.roleSelector{
    width: 75px;
   	height: 26px;   	
   	overflow: hidden;
   	background: url(http://zachetik.com.ua/static/images/new_arrow.png) no-repeat right #fff;
   	border: 1px solid #dedede;
}

div.roleSelector > select{
    background: transparent;
   	width: 103px;
   	padding: 5px;
   	color: #6c6e6b;
   	font-size: 14px;
   	line-height: 1;
   	border: 0;
   	border-radius: 0;
   	height: 26px;
   	-moz-appearance:none;
   	-webkit-appearance: none;
   	-o-appearance:none !important
}