Since you have received a gift card specifically for Christmas gifts, it is intended to be used for Christmas. As the recipient, you therefore have until December 31, which is the last day to use it.
If you do not manage to use it before then, it cannot be extended.
Once you have redeemed your Christmas gift card, you will receive a new gift card (e.g. for H&M) with a different expiration date. This expiration date can be found at the bottom of your new gift card and in your order confirmation.
You simply need to redeem your Christmas gift card for the item(s) you want before December 31. The new gift cards you receive can be used in the new year without any issues.