From Discworld & Terry Pratchett Wiki
Clancy (i) - daughter of War
Clancy is War's daughter, appears in Interesting Times, and is portrayed as a spoiled little girl wearing a Pony Club hat. As the daughter of a Valkyrie, this is perhaps only fitting. She has a permanent scowl which makes her brothers Panic and Terror somewhat redundant at the moment.
Clancy's description evokes the work of British cartoonist Norman Thelwell, who specialised in drawing cartoons of serious, somewhat grumpy, Pony Club girls and their ponies, described as "fat little things with a leg at each corner" (a description used somewhat ambiguously - it isn't clear that this is just about the ponies). Thelwell's cartoons tend to depict mini-Valkyries getting into all sorts of equine scrapes, and there was a big vogue for them, among the horsy set, in the fifties and sixties.
Clancy's name is a likely reference to Tom Clancy, author of Cold War techno-thrillers.
Clancy (ii) - the butchers
Sidney Clancy (39) and Son, 11 Long Hogmeat, Purveyors of Finest Cat and Dog Meats To The Gentry.
Vetinari's pet-food retailer of choice for Wuffles and a lifesaver for Otto Chriek. However, there is a hint in Making Money that with the advent of a new pet dog, Clancy's may have lost the contract to a new supplier. Clancy's may not be too bothered about this. Mrs Bradshaw's Handbook informs us in the section on Shankydoodle that Clancy's have a long association with the racecourse here. The company sponsors a grandstand, and has an exclusive contract with the racecourse (and possibly others) to sensitively remove and reverently dispose of those horses that not even Doughnut Jimmy could usefully resuscitate. Unfortunate horses may be consoled by the thought their deaths were not in vain and they will be reverentially buried, after a short period of digestion, in somebody else's back garden by grateful cats.
Clancy (iii) - XXXX'ian
This Clancy is a stock man who works for Remorse in The Last Continent, and helps invent XXXX-ian slang. Well, he is frequently accused of inventing it and winging it when he doesn't know the correct slang term