FX is banking on the new “Star Trek” pic to play long and prosper for the cabler, which has picked up TV rights to this weekend’s box office champ.

In what’s said to be a standard four-year movie license, FX could pay Paramount as much as $24 million for the sci-fier — or about 12% of box office gross if it hits the $200 million threshold domestically.

“Star Trek” opened over the weekend with a three-day domestic gross of nearly $80 million.

As is also standard, Par retains the rights to carve in an opportunity for broadcasters to secure a run or two of “Star Trek” during FX’s window.

“Star Trek” will start appearing on FX about 30 months from now — in time for the 2011 holiday season. That’s after the initial pay TV window, rights to which are held by burgeoning premium cable outfit Epix, co-owned by Par parent Viacom, MGM and Lionsgate.

FX likely outbid the other two major cable movie buyers, Turner and USA (which might have been a good fit for “Star Trek” given its soon-to-be renamed Sci Fi sibling). All three cablers have been aggressive on the movie acquisition front in recent years.

“Trek” reps the third spring/summer 2009 box office champ to be snapped up quickly by FX, which has previously secured the network rights to DreamWorks Animation’s “Monsters vs. Aliens” and 20th Century Fox’s “Wolverine.” FX also has the rights to another likely smash, “Transformers: Revenge of the Fallen.”

FX secured “Transformers” as part of another pact with Paramount, which earlier this year sold the cabler a slate of theatricals that included “The Curious Case of Benjamin Button,” “Cloverfield” and “Tropic Thunder.”