The most obvious place to start is by adding a fence topper. They’re available in different materials and you could 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.
How you tackle a DIY railing extension will depend on your railing and the available materials. A good option is wood pallets, as you can get a lot of lumber from these.
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.