List sub-taxonomies from current taxonomy

This may help you:

<?php

//first get the current term
$current_term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );

//then set the args for wp_list_categories
 $args = array(
    'child_of' => $current_term->term_id,
    'taxonomy' => $current_term->taxonomy,
    'hide_empty' => 0,
    'hierarchical' => true,
    'depth'  => 1,
    'title_li' => ''
    );
 wp_list_categories( $args );
?>

Source – https://codex.wordpress.org/Function_Reference/get_term_by (You can hard code the “books” taxonomy or you can just get the active taxonomy).

EDITED

You can create a custom function for getting a taxonomy’s childrens just like on the below link.

$hierarchy = get_taxonomy_hierarchy( 'book' ); 

/**
 * Recursively get taxonomy hierarchy
 * 
 * @param string $taxonomy
 * @param int $parent - parent term id 
 * @return array
 */
function get_taxonomy_hierarchy( $taxonomy, $parent = 0 ) {
  // only 1 taxonomy
  $taxonomy = is_array( $taxonomy ) ? array_shift( $taxonomy ) : $taxonomy;

  // get all direct decendents of the $parent
  $terms = get_terms( $taxonomy, array( 'parent' => $parent ) );

  // prepare a new array.  these are the children of $parent
  // we'll ultimately copy all the $terms into this new array, but only after they
  // find their own children
  $children = array();

  // go through all the direct decendents of $parent, and gather their children
  foreach ( $terms as $term ){
    // recurse to get the direct decendents of "this" term
    $term->children = get_taxonomy_hierarchy( $taxonomy, $term->term_id );

    // add the term to our new array
    $children[ $term->term_id ] = $term;
  }

  // send the results back to the caller
  return $children;
}

http://www.daggerhart.com/wordpress-get-taxonomy-hierarchy-including-children/

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