1A bill or invoice; the amount owed for purchases or services (often 'tsuke' for credit/charge to pay later).
居酒屋で飲んだ分は、月末にまとめて付けで支払うことにしている。
I arrange to pay what I drank at the izakaya in a lump sum at the end of the month.
レジの女性に『ツケでお願いします』と言ってしまった。
I ended up saying to the cashier, 'Please put it on my tab.'
彼は飲み代を店に付けにしていたが、先週まとめて支払った。
He had his drinking expenses charged at the bar, but he paid them off last week.
2A tab or credit — an entry recording a purchase to be paid later; using credit at a shop or restaurant.
この八百屋は顔馴染みならツケをきかせてくれる。
This greengrocer gives regular customers credit (lets them put things on the tab).
締め日に店から付けの明細が送られてきた。
A statement of the items on the tab was sent from the shop on the billing date.
3In board games (e.g., go), 'tsuke' is an attaching move — playing a move that attaches to the opponent's stone or piece; the attachment move itself.
この局面では黒の『付け』が有力で、白は苦しい。
In this position, Black's attach (tsuke) is strong, and White is in a difficult spot.
4A sound effect in kabuki and other traditional performing arts — the sound produced by striking wooden clappers or boards (often written 'ツケ').
名場面で拍子木の付けが入り、場の緊張感が高まった。
At the famous scene, the clappers' tsuke sounded, heightening the tension.
5Archaic: a letter — an old word for written correspondence, now rarely used.
（古文）先日の付けは到着したか、との書簡が残されている。
(Classical) A letter remains asking whether the aforementioned missive has arrived.
6Archaic: a reason or pretext — used in older texts, not common today.
（古文）行かぬ付けを並べてはならぬ、との戒めが書かれている。
(Classical) A warning is written not to list false excuses for not going.
7Archaic: one's fortune or luck — a term seen in old writings and rarely used now.
（古文）あの者の付けは悪し、との記述がある。
(Classical) There is a note saying that that person's fortune is bad.