I am trying to change the HTML "select" tag's default arrow to the one similar in the photo attached. Any ideas please?
Here's a pure CSS solution: You could hide the default arrow and display another one using a background image. This is an example which you can customize based on your needs.
select {
width: 100px;
padding-left: 5px;
border: 1px solid #ccc;
height: 25px;
-webkit-appearance: none;
-moz-appearance: none;
appearance: none;
background: url(http://www.stackoverflow.com/favicon.ico) 95% / 20% no-repeat #fff;
}