In a parallel universe, Starfleet was a uniformed service of the United Federation of Planets during the 23rd and 24th centuries.
The Federation and its Starfleet were well established by the year 2267 in the 23rd century. It was represented by the Constitution-class vessel USS Enterprise (NCC-1701). (COMIC: Assimilation²)
In 2368, when Delta IV was attacked by the Borg-Cyberman Fleet, it was Starfleet which organised the defence and evacuation of that Federation world. (COMIC: Assimilation²)
In an alternate timeline, the Cybermen, after integrating N-Space with the Federation universe, successfully conquered Mutter's Spiral. Several points in this timeline were visited by the Doctor's TARDIS, as the Eleventh Doctor demonstrated to Captain Jean-Luc Picard what would happen had the Cybermen been allowed to conquer the Borg. After conquering the Borg Collective in the late 24th century, the Cybermen began a campaign to convert the galaxy. By 2533, the Cybermen had conquered Earth and vanquished San Francisco's Starfleet Academy, the last holdout of free humanity. (COMIC: Assimilation²)
Owen Harper jokingly told James Mayer that Jack Harkness was calling Starfleet about the alien warning device Torchwood Three had in its possession. (PROSE: Border Princes)