First just because it once existed doesn't mean it still does. I mean how many years has it been since we heard of a ruling Earth Body? Early first season TOS, and most of that was in reference to a Space Agency and such, not necessarily a governing body.
And of course most of those references were due just because the writers of TOS had yet to come up with Starfleet, and the Untied Federation of Planets. I think its only pre Federation Enterprise that consistently uses an Earth based governing body.
For example we see no Earth government during the Probe's attack on Earth in Star Trek IV. All the decisions we see made are by the Fed President and the head of Starfleet. Nor do I believe we see any representative of an earth based government in the Motionless Picture. I believe those are the only TOS era events to threaten Earth, that we see before TNG.
Based on what we do know I think its safe to say that the Federation and Starfleet seem to be the ones in charge when at the very least it comes to outside threats.
There is probably a local governing body that handles internal earth issues, and even military forces or security forces for internal earth issues, or to supplement Starfleet. But I don't think after ENT we have any evidence of a local Earth Government that has say on External Security issues that face earth.