Possible Clues:

• At the end of which the beast might be found
• Rope to fasten or restrain animal
• After short time, anaesthetic that restricts movement
• Rope; the exasperated at the end of it
• That's enough to get a hold on you and put you to sleep at last
• That'll have you on hold and asleep in the end
• It might be a tie that would put one to sleep after tea
• Tie up an animal
• Rope for tying animal
• It gets a hold you and puts you to sleep at last