Fetching details from the dictionary...

to succeed (a person, to a position, etc.); to inherit; to take over; to follow
to patch (clothes); to mend; to repair
to add (e.g. charcoal to the fire); to replenish with; to feed with; to follow up with (e.g. remarks); to gather (one's breath)
長男が家業を嗣ぐことになった。
The eldest son will take over the family business.
彼は家業を嗣いで成功した。
He succeeded in the family business.
王位を嗣ぐ者が決まっていない。
The successor to the throne hasn't been decided.