(written from a Production point of view)
National Amusements was founded in 1936 by Michael Redstone as the Northeast Theatre Corporation and has since gone on to become one of the world's leading media companies with more than 1,500 movie screens and controlling interests in CBS Corporation and Viacom, the current owner of Paramount Pictures.
As the conglomerate is fully owned by "media mogul" Sumner Redstone (son of founder Michael, and until 2016 also the CEO of both Viacom and CBS) and his daughter Shari, this means that the Redstone family is presently the de facto legal majority owner of the entire, official Star Trek franchise, since the acquisition of the franchise in 1994 by the "old" Viacom, Redstone had already acquired previously. Sumner Redstone incidentally, had engineered the 2005 "old" Viacom split into CBS Corporation and "new" Viacom, which became effective in January 2006. The position of identifiable individual legal majority ownership of Star Trek had previously been held by the Charles Bluhdorn family (1967-1994), and before that by Lucille Ball (1964-1967; Gene Roddenberry lost all rights and title to his creation the moment he sold his Star Trek is...-pitch to Ball's company, Desilu Studios, in April 1964 ). While the 2005 split resulted in the formal ownership transfer of the Star Trek franchise from Paramount to CBS, the ownership position of the Redstone family remained unchanged.
It should be noted that the conglomerate is skirting what is legally allowed. In 1948, the United States Supreme Court had its anti-trust ruling leveled against the motion picture industry – most ironically against Paramount Pictures in particular, being singled out by the Court as proxy for the entire industry – , specifically aimed at the time to break the top-to-bottom vertical hold individual studios hitherto had on the entirety of the industry, otherwise known as the traditional "Hollywood Studio System" (see also Desilu Studios and Universal Studios in this regard). With full control over both production and dissemination of their movie and television productions, the conglomarate as presently organized, is partially negating the intent lawmakers had in mind back in 1948.
After her father was forced to step down in 2016, officially for age reasons, and she became his successor, Shari Redstone – who had never been in favor of her father's 2005 split decision to begin with, but as minority shareholder was impotent to prevent the move at the time – has been trying to remerge the two entities, but found herself embroiled in a power struggle with CBS CEO Les Moonves who, as co-architect of the split, vehemently opposed the proposition. The struggle though, seems to be decided in Redstone's favor after the former was forced to leave CBS in the wake of the #Me Too movement controversies, Moonves found himself in as of July 2018, when The New Yorker broke the news of his alleged sexual harassment accusations – actually also unofficially part of the reasons why her father had to step down, as he too had not been free of similar accusations. Part of the severance agreement however was that Redstone had to cease her remerging efforts for at least two years. But while this at first glance may look like a concession on her part, it is actually more likely to make Redstone's mission stand a better chance to succeed, as the Board will have been purged from Moonves supporters by then, as is customary in such circumstances in not only Hollywood, but in other industries as well.  
If successful, this will for the Star Trek phenomenon – split up between the two entities in the 2005 "divorce settlement" – mean a "reunification" of the television and movie franchises.