Hi, Juli!
I've dabbled with making myself a Star Trek deck, too. I didn't intend for it to be published, though, since I was just doing it for my own enjoyment.
However, I've learned that Paramount is fanatic about keeping anyone else from using unauthorized images, and they rarely, very rarely, allow outside interests to create material based on the ST characters. I'm guessing that if you contact Paramount directly, not only will they say "No" but they will order you to cease and desist using any copyrighted images for any reason whatsoever. I'm not kidding...they are really obnoxious about this.
Do a Google search for "Star Trek" "Paramount" and "Letter" and you will see some of the letters people have received from Paramount about their websites. True, the web users were using pictures and sounds without authorization. But the restrictions Paramount demanded included NO synopses of plots or 'artistic images' based the various TV shows, which seems ridiculous to me.
Anyway, sorry I got off on a rant here! I guess I still have this lingering belief that Paramount somehow caused the hard drive crash I had a year ago that lost all the images of the Star Trek tarot cards I'd completed!
Also, most of this was going on a few years ago, and they may have relaxed somewhat since then.
Good luck on your deck!
Peace,
Melvis