simple tax_query intersection
As jdm2112 and SallyCJ said in the comments, the query lacks of ‘field’ => ‘slug’. So: ‘tax_query’ => [ ‘relation’ => ‘AND’, [ ‘taxonomy’ => ‘link-category’, ‘terms’ => $link, ‘field’ => ‘slug’ ], [ ‘taxonomy’ => ‘despacho’, ‘terms’ => $despacho, ‘field’ => ‘slug’ ], ],