How to get quote from checkout session?

Use below code

<?php
namespace Ngage\CheckoutModification\Block;
use Magento\Checkout\Model\Session as CheckoutSession;
class CheckoutQuote
{
    private $checkoutSession;
    public function __construct(
        CheckoutSession $checkoutSession
    ) {
        $this->checkoutSession = $checkoutSession;
    }

    public function getQuote()
    {
        return $this->checkoutSession->getQuote();
    }
}