It depends on what you want that arc to say.
An arc should say "something" even if it's something basic, because then you have a goal to meet that message. If you can't think of what to say, have a goal, at least.
Here's an example:
I want a pompous character to think about their actions and mindset and become more level headed. How?
Setting: Let's say this character is very egoistical because they're a very good cook, and they know it. Because of this, let's make the setting a cooking competition.
Climax: The buildup factors into this. Because I thought of this example right now, it's very cliche, but who cares. There's a coolheaded person who's in the competition right next to him, and he's slowly getting more and more intimidated. This builds until he keeps doubting himself and eventually fails. To make it more interesting, there can be moments where it's clear that our main character is going to win, but then something goes wrong. Anyways;
Memorable ending: Our pompous character quits cooking altogether, and becomes a shut in.
You can stretch this arc into this character recognizing their bad behavior and taking steps to change it slowly, or you can have them become worse. Either way, our arc accomplished it's goal: make this character think about their ego.
This arc is in no means perfect, and this is a first draft, but hopefully this helps! 
