Suppose you have a custom taxonomy called “genre”, replace {$this->screen->taxonomy} with the name of the custom taxonomy i.e. “genre”

// Add info to the new columns
add_action( 'manage_genre_custom_column', 'wpdocs_show_genre_meta_info_in_columns', 10, 3 );

function wpdocs_show_genre_meta_info_in_columns( $string, $columns, $term_id ) {
    switch ( $columns ) {
        // in this example, we had saved some term meta as "genre-characterization"
        case 'characterization' :
            echo esc_html( get_term_meta( $term_id, 'genre-characterization', true ) );
        break;
    }
}

The sample below is for adding the column title in the same taxonomy.

add_filter( 'manage_edit-genre_columns', 'wpdocs_add_new_genre_columns' );

function wpdocs_add_new_genre_columns( $columns ) {
    $columns['characterization'] = __( 'Characterization' );
    return $columns;
}