Nothing will get your posture improved quicker than developing exceptional balance.
What this is good for:
Balancing exercises work your core muscles, lower back, and legs and promote alignment as your body needs to be in classically correct positions to avoid toppling over.
How to practice:
There are many ways you can practice improving your balance, and indeed you should explore as many as possible.
A great starter though is the one-legged stand. You can do this using the back of a chair or even the wall to begin with, using your hands to centre you. From there, you can then move on to versions where your hands are free, and you can experiment with trying to lean and move around whilst on one leg, a bit like you might imagine being on a tightrope.