Clifford R “Cliff” Dapper was born on January 2, 1920 in Los Angeles, California. The 18-year-old catcher signed with Bellingham of the Western International League in 1938 and played 46 games, batting .217.

He joined Hollywood of the Pacific Coast League in 1939 where he would remain for the next three seasons. Dapper played 125 games for the Stars in 1941 and batted .277 with eight home runs and 63 RBIs. 

He joined the Brooklyn Dodgers for spring training in 1942 and, during a pre-season game against the Reds, he was hit in the back of the head by a ball thrown by Cincinnati shortstop Eddie Joost. Nevertheless, Dapper was with the Dodgers on opening day and made his major league debut on April 19 against the Phillies.

Dapper spent the rest of the month in Brooklyn, appearing in eight games and batting .471 with nine RBIs before being sent to Montreal of the International League as a replacement for Herman Franks who had been called into the Navy. Dapper batted .224 for Montreal in 101 games.

Dapper entered military service with the Navy in late 1942 and was stationed at Los Alamitos Naval Air Station in California, where he regularly played baseball for the air station team in the Long Beach Recreation League during the winter months along with Bob Lemon and former Montreal teammate Jack Paepke.

On April 11, 1943, Dapper was selected to play for the Service Stars, along with Joe DiMaggio and Red Ruffing, against his old club, Hollywood. The servicemen beat the Pacific Coast League team, 5 to 2.

Dapper and Jack Paepke were assigned to the Naval Training Station at San Diego in 1944. The following year Dapper was sent overseas to Hawaii, where he was stationed at Aiea Barracks and reunited with Bob Lemon.

Dapper was discharged from service in December 1945. He played for Mobile of the Southern Association in 1946 and 1947, and continued to play in the minors with Atlanta, Hollywood, Eugene, Billings and Salt Lake City until the late 1950s.