Rearranging the letters of 'While the cat's away, the mice will play' gives:
With what aim? Well, A cheese, typically!
(by David Bourke by hand) (2000)
Other related anagrams without their own page:
"Rodentia" -> "I'd one rat." (by Segura using Anagram Genius) (2002)
"The American poet Thomas Stearns Eliot" -> "He promotes one theatre animal ... It's "Cats"!" (by Adie Pena using Anagram Genius) (2008) (pending approval)
"Book by old egg" -> "Gobbledygook." (by Jim Banholzer) (2018) (pending approval)