1. Your sister is entitled to equal share in your father's HUF, as per the amendment to the Hindu Succession Act, 1956 in 2005.
2. Being older son, you can't become Karta in your father's HUF automatically, since your sister is also a coparcener as per amendment to the Hindu Succession Act, 1956 in 2005.
3. Since daughters are also coparceners on par with sons for the property, you can't take independent decision to lease the HUF property to your cousin.
4. Daughters are also entitled to equal share in the HUF property on par with their brothers. However, voluntarily sister can execute a registered Release Deed relinquishing her individual share in favour of her brother. By this way, you can retain the property as sole owner of the property.