"长子继承权" can be translated into English as "primogeniture" or "the right of primogeniture".
"Primogeniture" refers to the system or right by which the oldest son inherits the entire estate of his parents or ancestors, to the exclusion of younger siblings or other relatives.
"The right of primogeniture" explicitly emphasizes this legal or customary right.
Both expressions are commonly used in legal, historical, or sociological contexts to discuss inheritance practices.