Praise be to Allah The Lord of the Worlds. And may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Married sister is either self-sufficient or non-self-sufficient by the financial support from her husband:
1. If she is self-sufficient by the financial support she receives from her husband, it isn`t permissible to give her Zakah money assuming that she is poor and needy. However, it is permissible to give her that assuming that she is one of the other categories eligible to receive Zakah, such as debtors. Self-sufficiency encompasses her basic needs from food, drink, clothing, lodging and medication. As for personal expense, it is a luxury rather than self-sufficiency. Kindly refer to " [Tohfat al-Mohtaaj, vol.7/pp.152] by Ibn Hajar.
2. If husband`s financial support doesn`t suffice her basic needs due to his poverty or stinginess then it is permissible for the brother to give her Zakah money. Rather, she is more entitled to this money than anyone else. Here, the Sadaqa (charity) given to a relative serves a double purpose, being both Sadaqa and connecting kin relatives. For more details, kindly refer to the book " [Fatawa Al-Ramli, vol.3/pp.142].
It is worth reminding that relationship with one`s sister shouldn`t be limited to giving her Zakah money; rather, one should connect with her as customarily practiced. And Allah The Almighty Knows Best.