During the initial appearance of Quirks, the Police Force did not enlist any officers with Quirks because they feared the superpowers may be used as weapons. Pro Heroes arose to fill the role of Quirk-wielding crime fighters. Police Officers now serve simply to arrest criminals that have been subdued by Pro Heroes while providing general support and enforcing low-level crimes.
The Police arrested Nomu and several dozen criminals following the U.S.J. Incident. They also debriefed the students before allowing them to return to U.A. Detective Tsukauchi launched an investigation on the League of Villains shortly afterward. He discovered that Nomu is an artificially enhanced human who was given multiple Quirks through All For One's Quirk. 
Chief Kenji Tsuragamae visited Izuku, Tenya, and Shoto in the hospital after they defeated the Hero Killer in Hosu. He reminded the U.A. students that it's illegal for them to use their Quirks to fight while still unregistered heroes. The Chief pardoned them for their crimes and then thanked the students for bringing the scourge of Stain to an end. 
Naomasa and the Police Force joined forces with the top Pro Heroes to form the Hideout Raid Team. This team's mission was to rescue Katsuki Bakugo from the League of Villains and to arrest Tomura Shigaraki and his followers. In less than a few days, the Police were able to ascertain the identities of Atsuhiro Sako, Jin Bubaigawara, Himiko Toga, Shuichi Iguchi, and Kenji Hikiishi. The villains eventually escaped after All For One attacked along with Nomu. All Might defeats All For One and the Police arrest him before placing him in Tartarus prison. 
Battles & Events
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