WordPress: Exclude the most recent post from the main query without braking pagination.

functions.php

<?php

// ...

/**
 * Tweak Archive pages queries.
 * @param object $query
 * @return object
 */
function tweak_archives( $query ) {
     		// If this is a Story Type term archive page.
		if ( !is_admin() && is_tax( 'story_type' ) && $query->is_main_query() ) {
			// Exclude the latest post from the main query without braking pagination.
			$ppp = get_option( 'posts_per_page' );
			$offset = 1;
			// Detect and handle pagination...
			if ( $query->is_paged() ) {
        			// Determine page query offset (offset + current page (minus one) x posts per page)
				$page_offset = $offset + ( ( $query->query_vars['paged'] - 1 ) * $ppp );
        			// Apply adjust page offset
				$query->set( 'offset', $page_offset );
			} else {
        			// This is the first page. Just use the offset...
				$query->set( 'offset', $offset );
			}
		}

	return $query;
}
add_filter( 'pre_get_posts', 'tweak_archives' );


/**
 * Adjusting the offset pagination on the Story Type taxonomy archive.
 * @param int $found_posts
 * @param object $query
 * @return int
 */
function adjust_offset_pagination( $found_posts, $query ) {
	$offset = 1;
	if ( !is_admin() && is_tax( 'story_type' ) && $query->is_main_query() ) {
		$found_posts = $found_posts - $offset;
	}

	return $found_posts;
}
add_filter( 'found_posts', 'adjust_offset_pagination', 10, 2 );