Advancing levels in training

Wasn't sure how to put this, but I don't know how to advance my levels in training. I'll train a horse, and for example in endurance I'm currently:

Endurance Progress:
Grade: local
Experience: 1192 (100%)
EXP required: 300
EXP left: -892

I can clearly advance to the next level, but I don't see what button I'm supposed to press to do so.
Thanks in advance!

I think you're looking at the Arena progress where you're training your horses. In which case that's solely the arena and property of the stable owner that owns it so they're the only ones able to upgrade the arena! It actually has nothing to do with your horse and won't affect your horse at all!

Your horses training level advances automatically each time you train your horse for a maximum of 5 levels. 
The Stat Boost points below that fill up one for every training to 10 and then you have to use them before training your horse again. 
The experience you get from training a horse in an arena of the correct discipline and/or grade is member experience that contributes to your account. 

Hope that helps clear things up, please ask if you have more questions!

Oh ok, thank you! I must've been looking at the arena progress.

That clears up other questions I had about how training works as well.