Couple minor things; after the big stuff, it's the little stuff that affects your story the most
commander of its fighter squadron is soon to be general Peter Halcyon.
"Commodore Halcyon" would probably work better, although SF and navy ranks seem to be interchangable. Also, unless Halcyon skipped a grade he'd be a Brigadier, not a full General.
The Claw is slated to return to Trojan IV Shipyards in the Trojan system next month so that the valiant carrier can be repaired and overhauled and its crew get some much needed shore leave.
As I mentioned, the Trojan IV shipyards are in Sol, not the Trojan system.
as a one hundred year old bottle of champagne
This sounds odd It would sound better, IMHO, if you wrote " a vintage 2551" or whatever instead.
Dreadnoughts don't have an X designation ... that's reserved for megacarriers int he prophecy era. Also, it's generally regarded that the Confederation is the CVS-14 (although that's far from official).
A klaxon sounded and Thrakhath looked on
I'd write it as "As the klaxon sounded, Thrakkath looked on", but again, this is a matter of opinion.
The Prince watched as the fighters vanished.
Into the distance or literally vanished?
The deck burst into applause and roars.
Kilrathi generally don't applaud ... they shout and rip open their veins as a ceremonial offering to the war-god Sivar
their boxy craft vanishing into the void.
"Boxy"? More like "sleek", perhaps?
according to a recent scout that sighted the ship.
The last part (that sighted the ship) is redundant, IMHO.
He swings his arm to cover his mouth, tapping the control stick and causing the damaged wire to swing back in contact with the circuit board. After sending the message, “For Kilrah” to his comrades, he rests back in his seat. He glances towards the tactical console and wonders. , “ Should I engage the backup system? The Prince would be most displeased if his cousin and most trusted pilot could not destroy his target because of a glitch.”
He toggles the switch and the resulting spark from the wire causes the console to explode, showering his face with glass and sparks. He cries out in agony and thrashes his arm around. He knocks the stick to the side causing his fighter to collide with his wingman. The last thing Khasra saw was a bright flash as his torpedoes explode, vaporizing him and both his wingman into tiny particles.
As Dralthi noted, switching tenses in the middle of the story isn't the wisest thing to do
He then became horrified as he heard the voice of the Claw’s comm officer clearing him in.
It'd be more immersive, I think, if you actually showed the comm officer responding ... somethign like this:
“No one will be there Chris, the Claw is gone!” he laughed.
He stopped abrubtly as a familiar voice resounded in his headphones."Tiger's Claw to Maverick, you are cleared to land. Welcome back".
Jazz gasped in horror. "This is impossible! The cats have screwed up again".
In general, you could also use more use of adjectives and color and visual descriptipns... like "Captain Zach “Jazz” Colson leaned back in his chair, a wicked grin on his handsome features". Something like that. It makes things more immediete and acts as a useful visual aid. Generally, this is a good first draft, though, and the good thing about the small things is that they can be worked out later.
