Greayer Clover was born on April 14, 1897, in Chicago, Illinois. He was the son of Samuel T Clover and Mabel Hitt Clover.

After graduating from Los Angeles High School in 1915, he entered Yale University but left his sophomore year to join the American Field Service as an ambulance driver. He persuaded five classmates to join him in this venture. In France, he served six months in the French Army, seeing active duty in the trenches as Fort Malmaison was recaptured. On the United States' entry into the war, he joined the American service and began training as an aviator. He fell on a formation practice run on August 30, 1918.

What would eventually become Santa Monica Airport was originally named Clover Field in his honor. Santa Monica does retain Cloverfield Avenue, recalling the airport's original name.

Greayer's Oak Park, in his honor, is located on North Figueroa Avenue, where a group of childhood friends planted an oak tree in his honor in the early 1920s. On present-day maps, the name is often incorrectly given as "Greaver."