Correct and elegant ballet arm positions depend on correct spinal posture, correct hold on the turnout, and correct placement of feet on the floor (and knee positions, if you are hyper-extended).
It sounds complex, but ballet body posture is natural and allows for relaxed movements of the neck, head and arms.
Following are a few tips so that you know how to improve.
When you, especially if you are an adult beginner, learn ballet, there is a lot of information to absorb about basic positions.
All ballet exercises depend on your understanding of, and ability to execute natural correct posture.
Other elements such as turnout, and safe stretching, follow as you progress in your dance classes.
When you stand up straight, yet relaxed, do your shoulders rest at the side of your torso, or do they curve into a "round-shoulders" position? A stretch you can do easily every day will allow your shoulders to rest below your ears.
Get a picture taken of you from the side.
Draw a vertical line through it, and see if your ears/shoulders/waist/hips/knees and ankles line up (or slightly forward from the ankles).
If those key joint positions fall behind or in front of the plumb line, you now can see what to correct.
Different styles of ballet teach different arm positions.
Regardless of the details, you want to attain a flowing, fluid quality from one ballet position to another.
If your hard work in ballet classes builds strength from correct posture, chances are that you will have elegant ballet arm positions that will improve your technique.
Ballet is an art form that increases the magical and imaginative dimension of life.
Understanding how to learn ballet brings you real physical results.
It's your journey, it's your dance.
Enjoy!