This is the classic delinquent TV show Sukeban Deka (スケバン刑事, 1985) starring Saitou Yuki.
Although it was released on DVD many years ago, it was only recently that it had a HD remaster re-run on the Touei channel.

Sukeban Deka S01 1985 720p HDTV AAC2.0 x264-JPTVclub
Subtitle: English

Drama: Sukeban Deka
Country: Japan
Episodes: 24
Aired: Apr 11, 1985 – Oct 24, 1985
Aired On: Thursday
Original Network: TV Asahi
Duration: 24 min.

mydramalist.com

Asamiya Saki was the ruling Sukeban of Takanoha Gakuen High which eventually led her to prison. Her mother was also incarcerated on death row – charged with the murder of her husband. Saki was then approached by Kurayami-Shirei with a deal – work for “The Cabinet” as an agent for the new “Sukeban Deka Project” and she and her mother would be freed – or she could just rot in jail. An offer she couldn’t refuse. Edit Translation

Sukeban Deka II: Shojo Tekkamen Densetsu (Japanese sequel)
Yo-Yo Girl Cop (Japanese adaptation)
Native Title: スケバン刑事
Also Known As: Delinquent Girl Detective
Director: Sakamoto Taro
Genres: Action, Thriller, Mystery, Tokusatsu

iNFO