Refers to inheriting a position, title, or family line, or the person who does so. Often used in formal or historical contexts.
彼は家督の嗣として育てられた。
He was raised as the successor to the family headship.
嗣がまだ決まっていない。
A successor has not yet been decided.
He became the previous head's successor.
一族は新たな嗣を立てることにした。
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.
your heir; his heir
heir
succeeding to a business; inheriting a trade
legitimate heir
heir; successor
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.