To tidy up, put things in order, clean up, or put away (transitive).
昼ご飯の後で台所を片付ける。
I'll clean up the kitchen after lunch.
子どもたちにおもちゃを片付けさせなさい。
Make the children put away their toys.
出かける前に部屋を片付けておいた。
I tidied the room before going out.
To settle, deal with, or resolve a matter; to dispose of something.
借金を早く片付けたい。
I want to settle my debts quickly.
面倒な手続きは私が片付けます。
I'll take care of the troublesome procedures.
先にこの問題を片付けてから話そう。
Let's deal with this issue first and then talk.
To finish or complete a task; to get something done.
今日はこの資料を片付けて帰ります。
I'll finish these materials today and go home.
急ぎの仕事を先に片付けた。
I took care of the urgent work first.
片付けてしまえば、気持ちも楽になる。
Once it's finished, you'll feel better.
To marry off (one's daughter) — used colloquially in some contexts; occasionally written 嫁ける.
彼女の両親は彼女をいい家に片付けた。
Her parents married her off into a good family.
昔は親が娘を片付けることが重要だった。
It used to be important for parents to arrange a marriage for their daughter.
To do away with someone; to bump someone off — a colloquial/strong expression often implying elimination by force or wrongdoing.
あの組織は敵対勢力を片付けたと言われている。
It's said that that organization eliminated the rival faction.
警察は彼が誰かを片付けた証拠を掴んでいる。
The police have evidence that he got rid of someone.