The information below appears, in part, on the front page of the US Customs and Border Protection ESTA application page: esta.cbp.dhs.gov

"In accordance with Proclamation—Suspension of Entry as Immigrants and Nonimmigrants of Certain Additional Persons Who Pose a Risk of Transmitting Coronavirus effective at 11:59 p.m. eastern daylight time on March 16, 2020, the entry into the United States is suspended for most individuals, other than United States citizens and lawful permanent residents, who have been physically present within the United Kingdom and Ireland within 14 days of travel to the United States. In addition, Proclamation 9993 applicable to the Schengen Area, Proclamation 9992 for travel from Iran, and Proclamation 9984 for travel from the People’s Republic of China all remain in effect. Any traveler with a valid ESTA who attempts to travel the United States in violation of the Proclamations for the Schengen Area, the United Kingdom, and Ireland will have their ESTA canceled...."dom, excluding overseas territories outside of Europe, or the Republic of Ireland within 14 days of travel t
There is no cessation of the ESTA application process per se; but, depending on the travel routing and citizenship/resident status of the ESTA holder, the ESTA may be canceled.