How to add new payment to the Apple ID linked to Video Star Pro subscription?

Your sister is the Organizer of the Family plan and it is set up to use Purchase Sharing. Along with being able to share apps with each other, it all requires any purchase you make to be processed on the Organizer's Credit Card. The card your sister is using is no longer valid since a purchase was declined. Your sister will need to add a new card that is valid in order for you to make purchases. It may be possible for you to purchase a Gift Card and redeem it on your iPhone to add money to your Apple Account Balance. Any purchase you make will first be deducted from your Apple Account balance until it is empty, then will attempt to charge your sister's card.

It means you are part of a Family Sharing group and she is the organizer. Only the organizer can–and must–have a working card present for the group. Hers is apparently no longer working. Ask her to remedy that. While you can pay with personal balance, the card must be present and working.

You cannot add a card, only the organizer can. That's why I said she had to remedy it. If you wanted to use your own card you would have to leave the family group.

Right on!