Refers to inheriting a position, title, or family line, or the person who does so. Often used in formal or historical contexts.
He was raised as the successor to the family headship.
He became the previous head's successor.
A successor has not yet been decided.
The family decided to name a new heir.
That family line had no heir.
相続人 is the legal term for a person who inherits property or rights, whereas 嗣 focuses on succession of a position or family line rather than legal inheritance.
The kanji 嗣 is composed of 口 (mouth) and 冊 (book) with 司 (administer) as a phonetic component, originally meaning 'to inherit' or 'to continue'. The reading し is the on'yomi.