Get order carrier cost in prestashop

You want to get the order shipping cost, it's simple
You should use 

getPackageShippingCost($id_carrier)

function, i suppose that you have the id_carrier from the order
like this

$id_carrier = $order->id_carrier;
$id_cart = $this->context->cart->id;
$cart = new Cart($id_cart);
$carrier_cost = $cat->getPackageShippingCost($id_carrier);

This get the shipping cost with tax included.