Gould was born Clara Pitcher in Martinsburg, Lewis County, New York, USA, on 17 March 1879. Her parents were Herman Pitcher and Mary Hart. She rode a stagecoach with her parents to Earlville, where she graduated from high school as class valedictorian. Before her marriage, she taught for two years at a one-room schoolhouse.

On 29 December 1899, she married Elmer Could, who was a farmer at the time. They later moved to Waterloo, Iowa where her husband worked for the Illinois Central Railroad. The couple had four children (one daughter: Helen, and three sons: Roy, Everett, and Earl). The couple lived in South Dakota and Minnesota for some time before moving back to Waterloo to live with their daughter in 1963. However, her husband died the next year.

Her mother died at 97, and her younger brother died at 94.

On her 110th birthday, no party was held due to her poor health. She had just recovered from an unspecified infection. Her only surviving child, Helen Williams (aged 84 at the time), stated for newspaper articles how her mother was unable to see, talk or walk, and weighted only 70 pounds at the time of her 110th birthday.

Gould died in Cedar Falls, Black Hawk County, Iowa, USA, on 27 December 1989. She was survived by one daughter, nine grandchildren, 19 great-grandchildren, and 17 great-great-grandchildren.