Actually it depends on how far you want to go. You can jump to protected mode with a few lines more. But you won't have a very interesting exercise.

Basically, one would have to setup multiple registers like the GDT which sets the protection on different memory ranges (hence protected mode). Once you have your GDT setup, set a few bits in CR registers and execute a long jump to the code segment of the GDT (provided you have instructions loaded there).

Then once in protected mode, everything changes. The system allows you to set interrupts habdlndlers through the LIDT, to enable memory paging and you'll have to reload the GDT again. But no more access to the convenient BIOS functions.

You also set up the PIC of your system to get a ticking clock for scheduling your kernel operations. Once you got all that is where the fun begins and you can start implementing memory managers and allocators, writing a disk operations layer and implement (or write your own!) filesystem.

OS Dev is truly a fascinating subject because there's so much to learn. Even more with 64-bit, and multiple core initialization and usage.

I don't know how all of this works on ARM, but I might order myself an experimentation board to get my hands on.