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'
  ],
],

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