The Biden administration began its overhaul of Immigration and Customs Enforcement on Thursday by announcing that it will direct officers to focus primarily on certain groups of immigrants, such as those suspected of being a national security threat and recent border crossers.

The Biden administration had previously attempted a 100-day deportation moratorium, but that plan was blocked by a federal judge in Texas. The judge’s order, however, did not stop the White House from moving forward with changing ICE’s arrest priorities, which will likely lead to a cut in the...