Each rider gains experience from showing and winning shows and they gain skill points for all 3 ( or just one for SD trained riders ) ) disciplines via the weekly training.
The riders will level up whenever one of the discipline skills hit the 101/201/301 etc. points and they will retire when they reach 901 points or become 65 years old.
Depending on how you´d want to micromanage your riders, this could be useful informations or not.
I prefer if the riders have as much experience as possible and if they are probably training in a higher level than their horses - which means you better assign horses to them when the rider is "in the 90s" and will level up with the next training sessions for your top money earning horses.