The obvious answers are outside TV media.
Mass Effect 1, the video game, was originally conceived as a Star Trek game, but they couldn't secure the IP rights, so ended up pivoting to a new universe that feels Star Trek like. Play it on story mode.
In print, there are literally a hundred reasonable options, some more or less like different elements of Trek. A good choice (in my opinion) is The Spiral Wars -- rogue ship and crew, diplomacy, great combat, alien civilizations that are non-monolithic... Or CJ Cherryh's Alliance Union universe (a good entry point is Downbelow Station, a good overview of the universe) -- many different scenarios and topics and a lot of ethical dilemmas that would make Trek proud.
Of course, if TV is your thing, try out Babylon 5, Stargate, or Farscape. They all sort of start slow.