Yes, you can choose whether the card can be used for online purchases using the toggle in the manage section of the connected Space or when you set up the card.
If your child has set up an online payment using their card and needs to order a replacement card, they will need to change the saved card details at that merchant to make sure payments aren’t declined.
For online transactions that require authentication via 3D Secure, you will need to approve these payments using your Starling app.