On the selector .nav-tabs > li > a:hover
add !important
to the background-color
.
.nav-tabs{
background-color:#161616;
}
.tab-content{
background-color:#303136;
color:#fff;
padding:5px
}
.nav-tabs > li > a{
border: medium none;
}
.nav-tabs > li > a:hover{
background-color: #303136 !important;
border: medium none;
border-radius: 0;
color:#fff;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
<link href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" rel="stylesheet"/>
<ul class="nav nav-tabs" id="myTab">
<li class="active"><a data-toggle="tab" href="#search">SEARCH</a></li>
<li><a data-toggle="tab" href="#advanced">ADVANCED</a></li>
</ul>
<div class="tab-content">
<div id="search" class="tab-pane fade in active">
Aliquip placeat salvia cillum iphone. Seitan aliquip quis cardigan american apparel,
butcher voluptate nisi qui.
</div>
<div id="advanced" class="tab-pane fade">
Vestibulum nec erat eu nulla rhoncus fringilla ut non neque. Vivamus nibh urna.
</div>
</div>