Returns the primary term for the chosen taxonomy set by Yoast SEO or the first term selected.

get_primary_taxonomy_term.php

<?php
/**
 * Returns the primary term for the chosen taxonomy set by Yoast SEO
 * or the first term selected.
 *
 * @link https://www.tannerrecord.com/how-to-get-yoasts-primary-category/
 * @param integer $post The post id.
 * @param string  $taxonomy The taxonomy to query. Defaults to category.
 * @return array The term with keys of 'title', 'slug', and 'url'.
 */
function get_primary_taxonomy_term( $post = 0, $taxonomy = 'category' ) {
	if ( ! $post ) {
		$post = get_the_ID();
	}

	$terms        = get_the_terms( $post, $taxonomy );
	$primary_term = array();

	if ( $terms ) {
		$term_display = '';
		$term_slug    = '';
		$term_link    = '';
		if ( class_exists( 'WPSEO_Primary_Term' ) ) {
			$wpseo_primary_term = new WPSEO_Primary_Term( $taxonomy, $post );
			$wpseo_primary_term = $wpseo_primary_term->get_primary_term();
			$term               = get_term( $wpseo_primary_term );
			if ( is_wp_error( $term ) ) {
				$term_display = $terms[0]->name;
				$term_slug    = $terms[0]->slug;
				$term_link    = get_term_link( $terms[0]->term_id );
			} else {
				$term_display = $term->name;
				$term_slug    = $term->slug;
				$term_link    = get_term_link( $term->term_id );
			}
		} else {
			$term_display = $terms[0]->name;
			$term_slug    = $terms[0]->slug;
			$term_link    = get_term_link( $terms[0]->term_id );
		}
		$primary_term['url']   = $term_link;
		$primary_term['slug']  = $term_slug;
		$primary_term['title'] = $term_display;
	}
	return $primary_term;
}

Sample Usage

Display the primary category from the default WordPress category taxonomy

<?php
    // Within The Loop.
    $primary_category = get_primary_taxonomy_term();
?>

<div class="category">
    <?php echo  $primary_category['title']; ?>
</div>

Display the primary term from a custom taxonomy

<?php
    // Within The Loop so $post is the current post object.
    $primary_category = get_primary_taxonomy_term( $post, 'my-custom-taxonomy-slug' );
?>

<div class="category">
    <?php echo $primary_category['title']; ?>
</div>

Add a link to the primary category's archive page

<?php
    // Within The Loop.
    $primary_category = get_primary_taxonomy_term();
?>

<a class="category" href="<?php echo $primary_category['url']; ?>">
    <?php echo $primary_category['title']; ?>
</a>