The Hero Public Safety Commission (ヒーロー公安委員会 Hīrō Kōan Iinkai?) was a law enforcement agency responsible for managing the interactions between heroes and society as a whole and for investigating the most dangerous cases of criminality.
The HPSC was headed by a committee of non-heroes, to improve the balance of influence between heroes and regular members of society. The Commission was amongst other things a criminal investigative organization and responsible for many hero-related matters, including the Provisional Hero License Exam, which is administered on a biannual basis in June and September. Hero Licenses are awarded by the Commission to those who pass the licensing exam.
The Commission worked closely with the Police Force to coordinate hero teams, as was done in the Hideout Raid, with the Hideout Raid Team. The Commission was also known for handling heroes individually to investigate and solve dangerous cases, as they did with Hawks, commanding him to become a double agent and infiltrate the League of Villains.
According to Yokumiru Mera, the Commission was understaffed. This leads to Yokumiru being overworked during the preparations for the Provisional Hero License Exam, and thus extremely fatigued by the time he has to proctor it.
During the Paranormal Liberation War the Commission decided to invite Rikiya Yotsubashi to make a deal with him, while in fact they planned to arrest him. However, the Detnerat CEO turned out to be Twice's Double and managed to retaliate and cause some serious damage to the building and the President, before melting away due to Twice's death.
According to Hawks, the HPSC has essentially shut down due the deaths and/or injuries of many of the Commission's top figures, making it difficult to receive foreign aid since there's no one to finish the necessary paperwork. 
Although the Safety Commission had been trusted by society to keep the peace, in actuality, the organization had an underlying corruptness in its acts to protect society's image of heroes in order to maintain the status quo. They groomed Lady Nagant to become an assassin, secretly killing corrupt heroes and villains under the people's eyes, to preserve their peace. When Lady Nagant questioned about the morality of the actions and suggested being transparent, the previous President of the Commission threatened to silence her, resulting in his death, which was then covered up.
Hawks, as Lady Nagant's junior, was also put under similar training regimes, and is implied to have taken part in some of these immoral actions for the sake of the organization that raised him, which he remained conflicted about.