The Federation Police Force (also called Galactic Federation Police, Galaxy Federal Police, Federation Police or Federal Police) is a military organization founded by the Federation Bureau created specifically as a resonse to the Space Pirates' attacks on vessels. Despite being powerful a force, the vastness of space has made locating the Pirates extremely difficult, as such they and the Federation Bureau pay high prices to powerful bounty hunters to assist them.
Samus, along with Mauk and Kreatz, was once a member of the Federation Police and had Adam Malkovich as her CO. Eventually Samus left the police force to become a bounty hunter. Chief Hardy is the chief of the Federation Police.
The Federation Police decide to send Samus when they fail to take Zebes, and she succeeds on her own during her Zero Mission. At some point after these events, it was determined that the Metroids needed to be destroyed once and for all, so a team was sent to check on SR388. They then proceeded to lose a rescue party, another group of Federation Police, and even a platoon of heavily armed soldiers before determining that the Metroids were still alive and well, then deciding to enlist the help of Samus Aran. (These events are not to be confused with the original research team that first discovered and was subsequently killed by the Metroids or the second that was intercepted by the Space Pirates.)
The Federation Marines and the Galactic Federation Army mentioned in Metroid: Zero Mission and seen in the Prime series and Metroid: Other M effectively replaced the police for a time. However, in Metroid: Samus Returns, the Galactic Federation Special Squadron sent to SR388 is said to be a part of the police force.