So in Game of Thrones I know that The Mountain is older than The Hound; but as everyone knows, the Mountain is a knight. Many would say that the hound is also a knight but this isn't technically true (as he was never knighted, and famously doesn't accept the title "Ser"). Also, as far as I can tell the Clegane brothers have no cousins. I know a member of house Clegane sat on Tywin's war council at Harrenhal but I'm pretty sure he's dead. So is the Hound the Lord of House Clegane or am I wrong about General Clegane being dead?
It seems not.
The only misunderstanding is that a Knight cannot inherit lands2. The opposite is correct, a Knight can inherit the House's estate. For example Edmure Tully is a Knight, he is also the Heir Apparent of House Tully; in fact he becomes Lord Tully once Lord Hoster Tully (his father) passes away.
Therefore, Knight or not, Gregor is the Heir Apparent of House Clegane. Until his death at the hands of The Viper.
The only 'vows' which deprive you of inheritance are:
- The Night's Watch
- The Kingsguard - who's vows are modelled after the Night's Watch3; which Sandor has taken
- Maesters of The Citadel
- Those in service to the Faith of the Seven, including:
- Septons and Septas,
- Faith Militant
- High Septon and the Most Devout
- Silent Sisters
- See Lancel Lannister, who gives up his wife and Castle to join the Faith Militant
Which means that theoretically, since Gregor is dead and Sandor has given up his claim to his father's lands, House Clegane is extinct.
Or is it?
You see, traditionally, members of the Kingsguard have always been Sworn Knights first4, and seeing that Sandor is famously "not a Knight", it may be argued that he also was never legitimately a member of the Kingsguard, and can keep his claim to his father's estate.
“The king and council have determined that no man in the Seven Kingdoms is more fit to guard and protect His Grace than his sworn shield, Sandor Clegane.”
“How do you like that, dog?” King Joffrey asked.
The Hound’s scarred face was hard to read. He took a long moment to consider. “Why not? I have no lands nor wife to forsake, and who’d care if I did?” The burned side of his mouth twisted. “But I warn you, I’ll say no knight’s vows.”
“The Sworn Brothers of the Kingsguard have always been knights,” Ser Boros said firmly.
“Until now,” the Hound said in his deep rasp, and Ser Boros fell silent.
-A Song of Ice and Fire: Book One - A Game of Thrones, Chapter 50 (Sansa V).
Ultimately, it comes down to George R. R. Martin's words on inheritance:
The short answer is that the laws of inheritance in the Seven Kingdoms are modelled on those in real medieval history... which is to say, they were vague, uncodified, subject to varying interpretations, and often contradictory.
1. My break-down of the laws of inheritance in Westeros.