Hot actress Alice Eve is beaming up to the big-time. The star is negotiating to land a lead role in J.J. Abrams’ upcoming “Star Trek” sequel. Eve’s best known for playing sexy journalist and Adrian Grenier love interest Sophia Lear on the final season of “Entourage.” Paramount’s untitled “Trek” sequel comes out May 17, 2013. But Eve will launch onto screens before that in “Men in Black III” with Will Smith. A rep for the actress, and the studio, did not return requests for comment.