Yes, you can. When you buy a Gold subscription via the Wizarding World website, you will be given the option to purchase it as a gift. During the purchase flow you will be prompted to enter the email address of the recipient. Once purchased, they will receive an email with their Gold subscription code which can be redeemed online.
You can also purchase the Wizarding World Gold Gift Box in-store at the Warner Bros. Studio Tour London shop, in selected Barnes and Noble stores and via the Barnes and Noble website here.