As you have certainly seen in many occasions, the hands and the poles are very important to help you balance, so to improve balance, we simply take away these aids.
We can complicate it further by placing the arms in many positions, where they further hinder balance, but, beyond simple balance training, keeping the hands in different positions helps as either a cue (where are my hips pointing) or change you stance (hands on knees) etc.
Let's start with placing the hands on the knees.
Leave your poles with your partner or at the top/bottom of the run. Put the hands on your knees and keep them there the entire run. You could keep the poles in one hand, if you're comfortable.
Then progress to "hands on hip".
Hands on knees also has an effect of hunching slightly forward, while hands on hips has a great feedback effect and helps with hip awareness: if you pay attention, you will know if the hips rotate or bank into the turns, especially if you keep your elbows up and pay attention to them, so it's a great aid in developing separation at the same time.
Leave your poles with your partner or at the top/bottom of the run. Or keep them in one hand.
Place your hands on your hips and keep them there the entire run. Use it to "keep" the hips in place, facing down the hill, while the skis turn left and right. Keep the elbows up and forward - if possible, in your field of view, as opposed to back and out of sight.
The hands will direct awareness to the hips, so you are aware when they rotate into the turn and correct it, by counter-rotating them, so they face down the hill.
Start with braquage and pivot slips++ first - to have a strong coiling, where the skis turn across the slope and you focus on countering the hips so they're facing down the hill at all times. Then continue with skiing, where you again focus on getting the skis to come across the hill, while your hips counter-rotate, so they stay largely pointing down the hill.
Also, try both grips with this drill:
Hands on hips specifically can be further used to bring your attention to stabilizing the hips.
See more at hands on hips.
We you're comfortable, we can progress to skiing with the hands behind the back variety:
Leave your poles with your partner or at the top/bottom of the run. Put the hands at your back.
Careful how you interlock the fingers, so you can take your hands apart in an emergency.
It not only is a balance challenge, but it brings the hips slightly more forward, to compensate for the arms being back.
We you're comfortable, we can progress to skiing with the hands behind the head variety:
Leave your poles with your partner or at the top/bottom of the run. Put the hands behind your head.
Do not interlock the fingers, so you can take your hands apart in an emergency.
This set of drills is very important for your evolution as a skier, especially as beginners. We will mention it regularly here and you should do it twice as much.