Star Trek crossing over with DC isn't anything new, given that Green Lantern has already crossed over with Star Trek in the AOS Timeline. I want to put a spin on this idea with Superman in the Star Trek universe. There are many ways to incorporate such a big hero into a universe as big as Star Trek, but Superman by himself could make for an interesting dynamic with the crew of the Enterprise/Voyager/DS9 etc. For one, the world of Star Trek is exactly what Clark wanted from the human race at the end of the fourth movie in Reeve's trilogy. In fact, all Clark wanted was to help humanity achieve great heights and look beyond fighting themselves.
In this AU, Clark suddenly arrives in the world of Star Trek and sees how his dreams for the human race are now reality. How he could have gotten there could be various reasons ranging from being frozen in time, being lost in space for many years, etc. Nevertheless, Clark is now in the 24th century (or 23rd if you want to do TOS). Clark would not feel anything but immense happiness for the people of Earth, but it would not be without cost since Clark would also learn of the Eugenics Wars, Khan, World War 3, etc. Clark is also the only superhero in this reality for simplistic sake. It would also be heartbreaking knowing most, if not everyone, he knows is now gone due to the passage of time. The Federation would see Clark as a legend of the past and beg Clark to join Starfleet, but I don't see Superman joining any government, even Starfleet. In the comics, Clark regularly assists the U.S. government, so I could see Clark helping the Federation regularly with brokering peace treaties, helping squabbles, etc, but for the most part, unless in very dire circumstances, Clark would largely help anyone who needs it. I could see Superman getting into disagreements with Starfleet on who to help and who not to help. The possibilities are endless.
In terms of power levels and getting into conflicts, Superman is shown in comic books taking regular damage from ship fire and any other weapons that wear him down. Clark couldn't take on an entire fleet of Klingons, Romulans, Borg, etc so he would need to be very careful when choosing who to engage with. It wouldn't take a genius for every faction/civilization in Star Trek to figure out that Clark is vulnerable to kryptonite, putting everyone on equal fighting terms with Superman. Q would also take an immense interest in Superman and, much like Mr. Mxyzptlk, would take every opportunity to mess with Clark as much as possible. To summarize, Superman would no longer be invulnerable since everyone now has weapons to hurt him.
Clark's personal journey can go various ways, similar to themes the previous Superman movies addressed. Does this new setting even need a Superman? Does he do more harm than good? I could see Clark questioning whether it's worth it to even continue to be a superhero in the world of Star Trek. I could also see Clark butting heads with the higher-ups in Starfleet, getting into squabbles with Klingons, and The Borg wanting to add Clark to the collective; the possibilities are endless.
