What is the ruling on giving one's sister a club membership card to gain entry, knowing that the club prohibits this, and is it permissible for her to enter without a card if the employee does not request it from her?

You are not permitted to violate the club's rules which prohibit that, as it is considered an infringement upon people's rights and an unlawful consumption of their wealth. Allah Almighty says: "And do not consume your properties among yourselves through falsehood." It is obligatory to fulfill legitimate conditions in contracts, based on Allah Almighty's saying: "O you who have believed, fulfill [all] contracts," and on the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions."