1To succeed or inherit a person’s position, business, office, etc.; to take over or assume a role or tradition.
彼は父の店を継いで、経営を始めた。
He took over his father's shop and started running it.
王位を継ぐ者は厳しい責任を負う。
One who succeeds to the throne bears heavy responsibilities.
彼女は家業を継ぐ決意をした。
She decided to inherit the family business.
2To mend or patch (clothing), i.e. to repair by joining fabric pieces together.
古いコートの袖を継いで使っている。
I'm using an old coat whose sleeve was patched.
穴の開いたズボンを継いでもらった。
I had my ripped pants mended.
3To add or replenish (e.g., adding charcoal to a fire), or to follow up with/continue something (e.g., remarks); to supply or continue.
火が弱くなったので、薪を継いだ。
The fire got weak, so I added more firewood.
彼の説明を継いで詳細を述べた。
I followed up his explanation and gave more details.
4In the game of go, to connect stones; usually written in katakana as ツぐ in this context.
その手で相手の石をツぐことができる。
With that move you can connect to the opponent's stones.