Born in
Kenmare,
County Kerry, Palmer played at club level with
Killarney Legion and won a
County Championship medal in 1946. He first appeared on the inter-county scene as a member of the
Cork minor football team in 1945 before subsequently winning an
All-Ireland Junior Championship medal with Kerry in 1949. Palmer's performances in this grade resulted in an immediate call-up to the
senior team and he won the first of five
Munster Championship medals in 1950. He claimed his first
All-Ireland title after a defeat of
Armagh in the
1953 All-Ireland final. After defeat by
Meath the following year, Palmer collected a second winners' medal after lining out at left corner-back in Kerry's defeat of
Dublin in the
1955 All-Ireland final. ==Honours==