What is the main conflict in Guards! Guards! by Terry Pratchett?

The city of Ankh-Morpork no longer has a king and is now ruled by a corrupt Patrician. A secret society calls a dragon with the understanding that whoever kills it will be named King and bring a new rule to the kingdom. Things go wrong when the dragon is crowned King of the city and the four members of the Night Watch Guard must keep the new king from eating the citizens.