Remove the taxonomy description field Drupal 7

The description field from taxonomy terms is a property of the taxonomy term entity and can't be deleted. It isn't a field coming from the field module but its values are stored inside the taxonomy_term_data table.

Hook_form_alter can be used to manipulate access to the field.

Use hook_form_id_alter(&form, &form_state, $form_id) to access the taxonomy term form.

This hook is placed inside a custom module.

Disable the taxonomy description for everybody

/**
 * Implements hook_form_FORM_ID_alter().
 */
function MYMODULE_form_taxonomy_form_term_alter(&$form, &$form_state) {
  $form['description']['#access'] = FALSE;
}
   

Disable the taxonomy description for everybody except the global administrator

/**
 * Implements hook_form_FORM_ID_alter().
 */
function MYMODULE_form_taxonomy_form_term_alter(&$form, &$form_state) {
  global $user;
  if ($user->uid != 1) {
    $form['description']['#access'] = FALSE;
  }
}
   	

Disable the taxonomy description for a certain role

/**
 * Implements hook_form_FORM_ID_alter().
 */
function MYMODULE_form_taxonomy_form_term_alter(&$form, &$form_state) {
  global $user;
  if (in_array('administrator', $user->roles)) {
    $form['description']['#access'] = FALSE;
  }
}
   	

Leave the taxonomy description enabled for administrators only

/**
 * Implements hook_form_FORM_ID_alter().
 */
function MYMODULE_form_taxonomy_form_term_alter(&$form, &$form_state) {
  global $user;
  if (!in_array('administrator', $user->roles)) {
    $form['description']['#access'] = FALSE;
  }
}