As a fellow
Star Trek aficionado, you'll find that there are quite a few RPG systems that capture the spirit of exploration and character-driven storytelling you're looking for!
First up, consider
Fiasco. It's a GM-less game that focuses on creating narrative-driven stories centered around character ambitions and failures, leading to dramatic and often hilarious outcomes. The playbooks provide various archetypes that could fit a Star Trek-like scenario, allowing you and your group to weave complex character relationships and plot twists that mirror the interpersonal dynamics found in Trek's episodes.
Another fantastic option is
Blades in the Dark. While it leans more towards the heist genre, its narrative mechanics and focus on crew dynamics can give you that sense of exploration and teamwork akin to the Enterprise crew. The game emphasizes character development, allowing players to grow their characters in meaningful ways, which is very much in the spirit of
Star Trek: The Next Generation narratives.
If you're open to a more traditional RPG, consider
Starfinder. It's set in a sci-fi universe and uses mechanics somewhat reminiscent of
Pathfinder but allows for space exploration and alien interactions. The character diversity and ship management systems make it possible to create rich stories full of exploration across different worlds, much like the voyages in Star Trek.
Lastly, I'd recommend checking out
Tales from the Loop if you're interested in a more indie take. While it's set in a retro-futuristic world, the themes of friendship, exploration, and adventure have that same heart that Trekkies love. Plus, the system is really accessible and focuses on storytelling.
Each of these games offers unique mechanics that encourage character development and exploration, making them great alternatives to
Star Trek Adventures. Enjoy your journey into new worlds! Qapla'!