A government by the nobles

One word substitute is Aristocracy.

Aristocracy: a form of government in which power is held by the nobility.
Democracy: a system of government by the whole population or all the eligible members of a state, typically through elected representatives.
Autocracy: a system of government by one person with absolute power.
Bureaucracy: a system of government in which most of the important decisions are taken by state officials rather than by elected representatives.