My first thought is - we are thrown straight into the action. We are not told how she got there, how this man is her rival and about this impending 'civil war'. Also, how she knew about the tiles. I am assuming most of those points you are going to elaborate on later, but others I guess you could incorporate into the text.
'But getting the crown out had taken a level of creative thought that Lyra was often labelled as incapable.'
I think you mean 'had often labelled'.
'...the side of the small, dusty trial.'
Self explanatory.
'She moved down the little used track to her draco'
I am guessing you could put a small clause in her rather briefly just the mean time due to the fact this is obviously a fictional (and probably draconian) race. Although described for Ri'ka, if remains a little too vague I think at the first mention of the beastie.
'The day that Ri’ka met destiny started off boring and dull.... he was in no uncertain terms, bored.'
Reuse in such a short space of words - perhaps substitute one?
'Behind the pair a group of guards came racing, six astride the black warhorses that Jaiol’s military preferred.'
I think there needs to be another comma to break up the six (or 'six of them') from the rest of the sentence, save it become a little ambiguous. Upon first reading I had to remind myself there wre not six of them to one horse.
A lot of the use of Ri'ka's name from 'Ri’ka had a moment of surprise', to 'Ri’ka found himself'.
'The momentum of the blow had sent Ri’ka spinning in his seat and completely dislodged the rider.'
'And had completely dislodged'?
All of what is happening with the collision if you wished to could be string together like consequences for effect. 'This happened, and then in turned this happened. Consequently this caused...' etc.
The girl fought with a cold, passionless expression on her face. Her blue eyes a furious expression of something caught between anger and some other emotion that Ri’ka could not identify.
'The girl fought with a cold...... Ri’ka could not identify.'
These two sentences could be merged else a small clause added to the second to help coherency.
'Dumped in a cell for as long as the captain of the guards, a Sir Orayn by the name, felt it would take Ri’ka to learn his lesson.'
Yet again, a bit of a broken sentence due to the one before it. If you changed it to 'stared through the bars', it should become more easy to understand, I think.
All in all, it is good, if but vague. If carried on, I should think a little explanation of prior action and some vague anaphoric references need to be outlined a little either as a next chapter, or placed in this chapter itself. It does however, make an interesting read.