Jeffrey was born in Bundanoon, New South Wales, to Susan (née Brody) and Thomas Hines; her father was a farmer.
After his death in 1931, she successfully petitioned the police commissioner, William MacKay, to allow her to join the force, despite being past the usual maximum age of application.
She was transferred to the Criminal Investigation Branch in 1935, and was "expected to concentrate her attention on the needs of women and children", taking statements from female witnesses in cases of rape, abortion, infanticide, and domestic violence.
Jeffrey was promoted to special constable (1st class) in 1943, and later became one of the first women to command an entire station, serving as officer-in-charge at Burwood (1946–1947) and Campsie (1947–1949).
Jeffrey lived at Jervis Bay in retirement, where she had a small poultry farm and orchard.