1To tidy up, clean up, or put away — to sort scattered things and return them to where they belong, leaving a place neat. The intransitive counterpart is 片付く.
遊んだあとは、おもちゃをちゃんと片付けようね。
After you're done playing, put your toys away properly, okay?
来客の前に、急いでリビングを片付けた。
I hurriedly tidied the living room before the guests arrived.
食事が終わったら、各自で食器を片づけてください。
When you've finished eating, please clear away your own dishes.
机の上が散らかっているので、少し片付けたほうがいい。
Your desk is a mess, so you'd better tidy it up a bit.
2To settle, resolve, or deal with a matter — to bring a problem, dispute, or debt to a conclusion.
借金を全部片付けるまでは、安心できない。
I can't relax until I've cleared all my debts.
その件は弁護士に任せて片付けてもらった。
I left that matter to a lawyer and had it settled.
厄介なトラブルを、話し合いでやっと片付けた。
We finally resolved the troublesome dispute through discussion.
3To finish, get through, or complete a task or errand — to get something done.
午前中に、メールの返信を全部片付けた。
I got through all my email replies in the morning.
溜まっていた宿題を一気に片付けた。
I knocked out all my piled-up homework in one go.
急ぎの仕事を先に片付けてから、昼食にしよう。
Let's finish the urgent work first and then have lunch.
4To marry off (one's daughter). A dated usage; today it sounds old-fashioned and is often avoided because it frames a daughter as something to be 「disposed of」. Occasionally written 嫁ける.
昔は、娘を早く片付けるのが親の務めだと考えられていた。
In the old days, marrying a daughter off early was considered a parent's duty.
三人の娘をみな片付けて、年老いた両親はほっとしている。
Having married off all three daughters, the elderly parents are relieved.
5(Slang) To do away with, bump off, or kill someone in the way — a strong expression used in criminal or fictional contexts.
「邪魔者は片付けろ」と、ボスは冷たく命じた。
「Get rid of anyone in the way」, the boss ordered coldly.
その筋の人間に頼んで、邪魔な相手を片付けたらしい。
He apparently hired an underworld figure to do away with the person in his way.