Originally Posted by Matth79
With a space elevator to get to the station, some form of army involvement would be reasonable, for staion security, and manning any defensive emplacements.
Also, secret service, if you take "Star Trek" for instance, even the "nice guy" Federation had section 31.
I think it depends on how things play out creating such a thing. Who owns the elevator itself? A corporation or a nation? The military itself? Multiple nations? You have to consider that to really figure out who is also involved in its defense. A corporation with the resources to build one on its own would also have the resources to secure it through private security. If the elevator is considered "public property" like roads, then it is unlikely that military is used as the first line of defense within the structure itself. Instead you will have a police force, with military handling the borders (Earth orbit). Multinational stuff gets really messy as you have multiple sovereign interests in the elevator.
Of course, this ignores governmental regulation coming into play, but the best example of that today is the TSA. Government organization in cooperation with police, but not military.
Still, I would expect that the military would have their own defenses for Earth orbit in general, rather than tacking onto the elevator itself. If you do that, and someone does
snap the cable, then your defenses get hurled out of orbit. Put your defenses close enough in geosynchronous orbit though, and even if you lose the elevator itself, you can still defend against threats.
One way to protect the elevator is to not make it a tastier target than it already is
Section 31 is more like a clandestine version of the CIA/MI5 and so on. Other fictional equivalents would be something like MI6 (James Bond). That kinda goes away from the idea of military service and structure. While NSA/CIA fall under the Department of Defense, they are not strictly military, and they tend to focus on intelligence. When it is time for force to be applied, there's military special forces that they can get cooperation from (see the Bin Laden operation for example).
I don't see military and national security folks actively engaged in the day-to-day of a space elevator unless the space elevator was built by the military for military use. I do expect that the military would be tempted by the idea of having their own space elevator though, so they can secure it for troop and supply movements to and from the surface. The expense might force them to not do that though, and instead use something similar to secured convoys on the existing elevator(s). They do that today on public roads, or even use troop transports along air routes.
derangedhermit has a lot of good ideas here, IMO.
As for how the military evolves, if I had to guess, this is what I'd see:
Navy - Evolves into a space-based fleet operations organization. Capital ships, carriers, etc.
Air Force - Evolves into a "planetary superiority" organization that focuses on space-to-surface operations. This includes fighters/bombers, troop transport and the like. Yes there is some overlap here as fighters and bombers are useful in space-based operations as well.
Marines - Evolves even more into a special forces organization, taking over most or all surface operations where you need boots on the ground.
Army - As the training required increases, and the need for surface operations becomes less of a focus, the Army withers. Eventually it is absorbed into the Marines along with the special forces from other branches that operate on the surface (i.e Navy Seals).
CIA/NSA/etc - This really depends more on the politics of the situation more than anything else. I'd fully expect intelligence to be a critical part, possibly remaining fairly autonomous from the military itself, identifying threats for the military and government to respond to. But otherwise, the political environment determines the shape of this beast more than anything else.
If something does happen involving the elevator though, there'd need to be more information on what the elevator is before you can start really digging into the interesting interplays. Did intelligence find a threat and the special forces are being brought in to handle a specific threat worthy of military intervention? What about having to work with the police force and the turf wars there? Etc. Etc.