Clarence begins life as a page in Arthur's court: "an airy slim boy in shrimp-colored tights that made him look like a forked carrot" (2.2). Luckily for him, he has an interest in strangely dressed oddballs and takes to chatting with Hank. He soon becomes the Yankee's stalwart sidekick, assistant, and boy genius, learning all of Hank's tricks and helping him build the schools and factories that will hopefully transform the kingdom.
Clarence doesn't show much in the way of personality. He's friendly, but kind of dim early on… like a lot of Arthur's subjects. For instance, he begs Hank not to put out the sun—"I implore thee remember my supplication, and do the blessed sun no hurt. For my sake, thy true friend" (6.4)—even though Hank hasn't shown any ability to do so yet.
Clarence takes to education quickly however, and soon turns into a clever engineer himself. This kind of makes him Hank's Mini-Me, and he acts much the way Hank does, though on a slightly smaller scale.
This transformation helps along a number of sticky plot situations when Hank needs someone to ride to the rescue or do things for him while he's inconveniently shackled in prison. It is Clarence, for instance, who sends the knights to the rescue on bicycles:
"Good deal of a surprise, wasn't it? I knew you'd like it. I've had the boys practicing this long time, privately; and just hungry for a chance to show off." (38.4)
We can see with this bicycle example too, that while Clarence does everything Hank asks him to, he can also march to his own beat and make his own decisions… which is good for Hank since he would have been killed otherwise.
Clarence comes to the Yankee's aid more than once, and stays loyal buds with him until the end. He even finishes up Hank's diary at the end, so we know what happens to him in Merlin's cave, saying "'I, CLARENCE, must write it for him'" (44.1). In this way, Clarence may be the only real hope at the end of the book. We don't know for certain what happens to him after Hank falls into enchanted sleep, and though it's implied that Clarence is going to die, he just might be clever enough to find a way out of the cave. In this sense, he makes for Hank's biggest success: an ignoramus whom he educates and turns into a better man.