Well, just a hunch but I don't think Lord Drinian or Jack will like each other much. Jack's but a breath away from anarchy (and arrogance) in Drin's opinion -- something he doesn't think particularly promising if they're to put Caspian on the throne.
Oh and, well, Jack would probably not like him because, for all intents and purposes, he's looking more or less like Miraz's minion right now.
This could come into play when Drinian is called to answer for a Narnian's death at camp. Drinian brought, unwittingly, poisoned vials of medicine to the Narnian camp. Drinian's own medicine (poisoned) was stolen from his belongings and mistakenly taken by a sick Narnian. Doesn't bode well. Jack could be a primary voice either for or against Drinian's innocence--whichever he's most likely to agree with-- in
this thread.
Could be a rather powerful first impression for Drinian.

Also, if any of the Telmarines becomes imprisoned (but perhaps that won't happen; though I don't see them letting the group go), someone would need to be the guard. The last prisoner they had escaped because of negligence. They'd probably put someone who is at the top of their game to guard the new one. That is, if and only if Drinian or any of his party become prisoners, though.

I just realised how many smilies I use! Wow.
On a side note, I'd imagine Drinian's somewhat of a prodigy with a sword. One doesn't get to be a captain in the armed forces at such an age without a good deal of skill.