update_user_meta doesn’t work with AJAX

First You can get rid of nasty globals in your AJAX call. I’m not sure what the $st variable that you were output is all about so I’ve excluded, but you can include as you wish –

add_action('wp_ajax_change_subscription', 'change_subscription');
function change_subscription(){

    if(!empty($_POST['term_id']) && !empty($_POST['type'])) :

        $user_id = get_current_user_id();       
        update_user_meta( $user_id, 'hannit_meta', 'My Value' );

    endif;

    die();

}

For testing, it looks like you were querying the meta incorrectly, so pleaes try this –

$user_id = get_current_user_id();
$tags = get_user_meta( $user_id, 'hannit_meta', true);
echo "<!-- u:".$user_id." val ".$tags."-->";