It's easy enough to get into investigating and improving your posture while you're static, but moving around is when it becomes critical. To address this, your instructor will show you "tai chi walking". This looks totally strange, but it really sorts out your posture, your balance, your awareness of where your weight is, your awareness of how you move and how to improve how  you move.

You absolutely need an instructor for this. Most people are very unaware of how they move and how they walk - after all, people have been doing this for decades already! So it's very hard for people to spot what they are doing, let alone what needs correcting while moving. Tai chi walking is something your instructor will not only show you, they will also show you how to change towards improving your posture for yourself while moving.

As you practise it, you will see the benefits of it posture-wise. It will really make you body-aware. If you also learn the tai chi forms, you will see how tai chi walking is at the basis of all of these. In fact, all the basic warm up exercises are extremely good for you in many different ways, which will become clearer as you continue practising them. Practising tai chi walking for 5 minutes every day, will sort out a lot of things, and especially help you improve your posture for yourself.