Actually Paramount does own the right to make a new star trek series or anything star trek. CBS never took over the ownership of star trek, they only took over the ownership of Paramount television division. But CBS does have the first dibs to have it air on CBS or the CW.
Sorry, but you have that completely backward. The company we now call the CBS Corporation is the same one that was called Viacom until the 2006 breakup, and in that breakup it retained the rights to all of Viacom's television properties, including Star Trek
. It didn't "take over" anything, because it's the same company under a different name. The company that's now using the Viacom name, and which owns Paramount Studios, is actually a new spinoff corporation, and it gained ownership of Viacom's motion picture properties in the breakup. Since ST was both TV and movies, Viacom/Paramount was granted a license to continue making ST movies, as long as it exercised that license within 18 months of the breakup -- which is why they got a Trek reboot underway in 2007, at a time when everyone was saying the franchise needed to rest for a few more years. But it is the CBS Corporation that owns the entire franchise.
Want proof? Look at the copyright notices. I'm looking at the DVD case of the 2009 movie, and in fine print just under the credits, there's a line that reads, "Copyright (c) 2009 Paramount Pictures. STAR TREK and related marks and logos are trademarks of CBS Studios Inc. All Rights Reserved." The novelization contains the same line on its back cover and copyright page except with "(c) 2009 CBS Studios Inc." inserted after the Paramount copyright. And if you look at any other post-2006 Trek novel or comic based on the original, non-Abrams continuity, the copyright notice mentions only CBS Studios, not Paramount at all.
Not to mention that the contracts I sign with Pocket Books for the Trek novels and stories I write refer to "the STAR TREK television series and/or motion pictures distributed by CBS Consumer Products ("CBS")." My last contract to mention "Paramount Pictures Corporation" instead was dated May 2006.
So it is CBS Studios (formerly known as Paramount Television) that owns Star Trek
in its entirety. The current Paramount Studios only has a copyright on the movie properties, but it's only allowed to use them under license from CBS, which owns the underlying concepts.