In cart_subtotal.tpl you get the smarty var value $newsubtotal and put it in a global php var $phpnewsubtotal.
Code:
{php}
global $phpnewsubtotal;
$phpnewsubtotal = $smarty->get_template_vars('newsubtotal');
{\php}
Then in cart.tpl you get the value from the php global var and put it in the smarty var.
Code:
{php}
global $phpnewsubtotal;
$this->assign("newsubtotal", $phpnewsubtotal);
{\php}
That's it I think. Be warned there is probably a more conventional way to do this as you will no doubt find out in subsequent replys by other folks.