1. Star Trek (2009): Michael Giacchino
2. Star Trek Into Darkness (2013): Michael Giacchino
3. Star Trek Beyond (2016): Michael Giacchino
4. Star Trek: Discovery (TV series - ongoing): Jeff Russo
5. Star Trek: Picard (TV series - ongoing): Jeff Russo
While Michael Giacchino composed for the three most recent movies, Jeff Russo is the current composer for the Star Trek franchise, as he composed the music for the *Star Trek: Discovery* and *Star Trek: Picard* series.