Raised in Phoenix, Arizona, Palmer is the middle child of five tennis playing siblings.

[2] A baseline player, Palmer made the singles fourth round of the 1962 Wimbledon Championships, beating Robyn Ebbern along the way.

She was a semi-finalist at the 1962 U.S. National Championships, with her performance including a win over the second seed Karen Susman.

She ended the year as the seventh-ranked player in the U.S.[3] Palmer was runner-up to Nancy Richey at the U.S. Women's Clay Court Championships in 1963.

[5] Palmer is considered by many, including journalist Bud Collins, as the first player on tour who would regularly grunt on shots.