Get the primary term of a post, by taxonomy. If Yoast Primary Term is used, return it, otherwise fallback to the first term.

functions.php

<?php

/**
 * Gets the primary term of a post, by taxonomy.
 * If Yoast Primary Term is used, return it,
 * otherwise fallback to the first term.
 *
 * @version 1.3.0
 *
 * @link https://gist.github.com/JiveDig/5d1518f370b1605ae9c753f564b20b7f
 * @link https://gist.github.com/jawinn/1b44bf4e62e114dc341cd7d7cd8dce4c
 * @author Mike Hemberger @JiveDig.
 *
 * @param string $taxonomy The taxonomy to get the primary term from.
 * @param int    $post_id  The post ID to check.
 *
 * @return WP_Term|false The term object or false if no terms.
 */
function jivedig_get_primary_term( $taxonomy = 'category', $post_id = false ) {
	// Bail if no taxonomy.
	if ( ! $taxonomy ) {
		return false;
	}

	// If no post ID, set it.
	if ( ! $post_id ) {
		$post_id = get_the_ID();
	}

	// Bail if no post ID.
	if ( ! $post_id ) {
		return false;
	}

	// Setup caching.
	static $cache = null;

	// Maybe return cached value.
	if ( is_array( $cache ) ) {
		if ( isset( $cache[ $taxonomy ][ $post_id ] ) ) {
			return $cache[ $taxonomy ][ $post_id ];
		}
	} else {
		$cache = [];
	}

	// If checking for WPSEO.
	if ( class_exists( 'WPSEO_Primary_Term' ) ) {

		// Get the primary term.
		$wpseo_primary_term = new WPSEO_Primary_Term( $taxonomy, $post_id );
		$wpseo_primary_term = $wpseo_primary_term->get_primary_term();

		// If we have one, return it.
		if ( $wpseo_primary_term ) {
			$cache[ $taxonomy ][ $post_id ] = get_term( $wpseo_primary_term );
			return $cache[ $taxonomy ][ $post_id ];
		}
	}

	// We don't have a primary, so let's get all the terms.
	$terms = get_the_terms( $post_id, $taxonomy );

	// Bail if no terms.
	if ( ! $terms || is_wp_error( $terms ) ) {
		$cache[ $taxonomy ][ $post_id ] = false;
		return $cache[ $taxonomy ][ $post_id ];
	}

	// Get the first, and store in cache.
	$cache[ $taxonomy ][ $post_id ] = reset( $terms );

	// Return the first term.
	return $cache[ $taxonomy ][ $post_id ];
}

Thanks, mate. Very useful

Just updated to add static caching for times when this function may be used multiple times for the same taxonomy/post_id on the same page.