The Galactic Police were organisations that enforced law throughout the galaxy.
Galactic law was enforced by several species, including the Megara, the Judoon and the Atraxi. (TV: The Stones of Blood, Smith and Jones, The Eleventh Hour)
The Shadow Proclamation was a galactic government concerned with upholding Galactic Law, as well as a set of rules governing it. In his ninth, (TV: Rose) tenth (TV: Partners in Crime) and eleventh incarnations, (TV: The Eleventh Hour) the Doctor called miscreants to account for themselves according to its dictates. The Shadow Proclamation used the Judoon as police. (TV: Smith and Jones)
The Slitheen initially thought Sarah Jane Smith was an agent of the Galactic Police in their first encounter with her. (TV: Revenge of the Slitheen)
Milo and Frank Shakespeare believed that the Eighth Doctor was an agent of the Galactic Police. (COMIC: Doctor Who and the Nightmare Game)