Remembered for her essays and short stories for The New Yorker, she penned numerous pieces that were later compiled in collections such as The Long-Winded Lady: Notes from the New Yorker (1969) and The Springs of Affection: Stories of Dublin (1997). Her sole novella, The Visitor, was published several years after her death.
After earning an English degree from American University, she began her journalism career with a copywriting position at Harper's Bazaar in New York City.
In Brennan's honor, Edward Albee named a character in his play Quotations from Chairman Mao Tse-Tung the "Long-Winded Lady."
The daughter of political activists Una and Robert Brennan, she spent her youth in Dublin, Ireland, and relocated to Washington, D.C. in her late teens upon her father's appointment as the Minister to the United States from the Irish Free State. Following a relationship with theatre director Walter Kerr, she married The New Yorker's editor St. Clair McKelway.
She was a cousin of fellow writer Roddy Doyle and is referenced in his book Rory and Ita.