The phrase "to take over the district" means to gain control or dominance over a particular geographical area, in this case, an entire district. Full definition
The state took over the district in 1995, to little effect. (educationnext.org)
Disagreement over the governance of Newark schools goes back more than two decades; the state took over the district in 1995 after documenting years of academic failure, unsafe buildings, corruption, and lavish spending by elected school board members. (educationnext.org)
Then Jerrick Cheeks, not a school dad but with child relatives in local schools, brought up other issues in a discussion on an article about school accreditation, and how some mostly white schools were allowed to keep their sports teams when the state took over the district while black programs were threatened. (hechingerreport.org)