It is. There's a few ways to go about it.
The easiest way is to just replace underused existing moves, like Bone Club and Mist Ball. This means less variety, and you have to be careful of hidden elements (replacing Sweet Scent could get you an unusual field move), but it requires little knowledge of the ROM's inner workings- just one of the many move editing tools out there. Most hacks go this route- it's fairly lazy these days in my opinion though.
The second way is to expand the move table. You can find a nifty tutorial on how to do that here:
https://www.pokecommunity.com/showthread.php?t=263479
Expansion is nominally harder but lets you retain all the old moves. I'd recommend it even if it seems difficult simply so you can get some hands-on experience with a hex editor.
In both cases, you'll want a way to edit your moves. I recommend the move editor here for that:
https://www.pokecommunity.com/showthread.php?t=311461
Personally I use Nightmare Table Editor, but this tool handles things in an easier to learn way.
For editing animations and creating custom move effects, I'd recommend looking around in the Research and Development subforum. There's a lot of useful stuff already built there, which should help you on your way to making your own battle scripts and animation scripts. Note that most reasonably complex moves, like Stealth Rock, Trick Room, and Natural Gift, will require you to write ASM- while this is less difficult than most people claim it's a daunting hurdle to overcome, so it'd probably be best to get some basic moves down first.