die Leine
leash
A long, thin rope or strap used to lead or tie up an animal, especially a dog.
Im Stadtpark müssen Hunde an der Leine geführt werden.
In the city park, dogs must be kept on a leash.

leash / line
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leash
A long, thin rope or strap used to lead or tie up an animal, especially a dog.
Im Stadtpark müssen Hunde an der Leine geführt werden.
In the city park, dogs must be kept on a leash.

When an animal is tied up or on a leash, you use the preposition 'an' with the dative: 'Der Hund ist an der Leine' (The dog is on the leash). When you put it on a leash, you use 'an' with the accusative: 'Nimm den Hund an die Leine!' (Put the dog on the leash!).
Mein Hund läuft im Wald immer ohne Leine, aber in der Stadt ist er an der Leine.
My dog always runs without a leash in the forest, but in the city he is on a leash.
'Leine' (line/cord) is often used as the base word in compound nouns to describe the function of the cord. Common examples are 'Wäscheleine' (clothesline), 'Angelleine' (fishing line), or 'Hundeleine' (dog leash).
Die Wäsche trocknet draußen auf der Wäscheleine.
The laundry is drying outside on the clothesline.
The idiom 'jemanden an der kurzen Leine halten' (to keep someone on a short leash) is fixed. The person being controlled is in the accusative. The adjective 'kurzen' is a fixed part of the expression.
Ihre neue Chefin hält alle Mitarbeiter an einer sehr kurzen Leine.
Her new boss keeps all employees on a very short leash.
ribbon / band
'das Band' and 'die Leine' can both mean something long and flexible that is used for tying or holding something. 'das Band' is usually flatter and often made of fabric, plastic, or metal. It is used for wrapping, decorating, or connecting things. 'die Leine' is more like a rope or cord and is typically used for dogs, laundry, or boats. The words can be confused if you only think of something long. A practical tip: for a dog or a clothesline, say 'Leine'; for a gift or a flat material, 'Band' is more likely.

Am Morgen hat sie den Hund an die Leine genommen.
In the morning, she put the dog on the leash.
Für das Paket braucht ihr ein starkes Band, damit es nicht aufgeht.
You need a strong ribbon for the package so that it does not come open.