While the official LEGO brand does not currently produce any Star Trek builds, there are compatible brick-building sets that have kits that are perfect for Star Trek fans. Note that these compatible systems generally use an inferior production process to genuine LEGO bricks, which may result in looser fitting clicks. However, these fun builds are generally highly rated and if you're building these for display rather than play, brick quality shouldn't be an issue. Here are some Star Trek LEGO-style builds.
This LEGO compatible build is a fun figure of Mr. Spock in the style of BrickHeadz models. The blocky design has a unique style; the head and arms are articulated for fun in display. This kit includes 133 pieces.
This is an awesome build of Star Trek's iconic starship that includes minifigures that can fit inside the saucer section! This is a 432 piece Star Trek brick build with minifigures of Captain Kirk, Mr. Spock, Dr. McCoy, and two blue-shirt crew members. This build also includes lights for extra authenticity.