just to get sure: you have no problem to show the gallery at the taxonomy page?
but you wish to show only the first image from that gallery?
have you try something like that?:
<?php
$images = get_field('gallery_images');
if( $images ){
$image_1 = $images[0];
}
?>
<a href="<?php echo $image_1['url']; ?>">
<img src="<?php echo $image_1['sizes']['large']; ?>" alt="<?php echo $image_1['alt']; ?>" />
</a>
