Get previous and next term from a taxonomy in WordPress. Use in a Taxonomy Archive.

taxonomy-archive.php

<?php
  
  $queried_object = get_queried_object();  // returns the current taxonomy term

  $my_taxonomy = get_terms("my_taxonomy", 
    array(
			'orderby' => 'name', 
			'order' => 'ASC'
		)
    
	);
	
	$previous_tax = false;
	$next_tax = false;
	$last_tax_in_loop = false;
	$passed_current = false;
	
	if( $my_taxonomy && is_array( $my_taxonomy ) ) {
		
		foreach($my_taxonomy AS $tax) {
			
			if($queried_object->term_id == $tax->term_id) {
				
				$passed_current = true;
				
				if($last_tax_in_loop) {
				
					$previous_tax = $last_tax_in_loop;
					
				}
				
			} else {
			
			
				if($passed_current && !$next_tax) {
				
					$next_tax = $tax;
					
				}
			
			}
			
			$last_tax_in_loop = $tax;
			
		}
		
	}