Welcome to the Spotify Community; I hope you enjoy your stay here, :).
I'm happy to hear you're currently a Spotify Unlimited/Premium subscriber, :). You should be able to redeem a gift card and not get charged at the end of your billing cycle. However, I'm not entirely too sure. I would suggest cancelling your membership (to remove your current card details), redeem your gift card, and then re-subscribe. This will make it so that your payment card will not be charged until the end of your current membership.
If you've got anymore questions, please don't hesitate to ask, :).