The most obvious place to start is by adding a fence topper. They’re available in different materials and you could even DIY one if you want.
If safety is your main concern, plexiglass panels are a good option. Find ones that are a foot or two taller than your railing and secure them in place with zip ties.
A wood lattice is a great option for how to increase the height of a balcony railing. You could add a small one to the top or use a larger one that reaches the balcony floor.
This option will, unsurprisingly, increase privacy on your balcony. A tall privacy screen also works well as a balcony railing height extension that doesn’t mess with the existing railing.
Hopefully, these ideas have given you some inspiration for how to increase the height of your balcony railing. Some options require drilling but whatever option you choose, make sure it’s secure!