for suppleness: work a lot on bending and stretching, you can do circles, spirals, serpentines, etc. also work on transitions a lot! :)
Is he a jumper? Small cross pole bounces are great to teach him to relax and just bounce through the cross poles helps keep straightness
You can work on transitions between ground poles for example, you will work the straightness and the reactivity which is very important for young horses. You can start with a wide space between poles, then reduce it. And vice versa, start with a reduced space between poles, and ad some space to see if your horse changes in its behavior.
For suppleness you can work on neck extension, it's so good for horses' back. You can start lateral movement but ask things slowly as it's totally new to them.
Hope it helps x