This short story is about a future emperor of the galaxy who is brought to Earth for what he thinks is a tour. A guide takes him around Earth on horseback and keeps saying “your life is in my hands”. The prince thinks the guide is security and he is there on a vacation. In reality the prince is being evaluated. In the end he turns out to be a coward and the guide has to kill him.
Gordon R. Dickson Call Him Lord. The visit to Earth is a kind of "manhood test" to reveal the Prince's suitability (or not) to be the next Emperor.
When the escort meets the Emperor, the latter demands to know how his son failed the test. After going over a few lesser problems, the escort gets to the heart of the matter, saying "Lord. He was a coward," and the Emperor of a hundred worlds recoils in shame.
This first appeared in the May 1966 Analog. There is a Wikipedia article about it.