In 1965, Closter's first year in the minor leagues, he split his time between two teams, the Rookie leagueJohnson City Yankees of the Appalachian League and the single-AGreensboro Yankees of the Carolina League. In the winter, Closter also spent time with the Yankees affiliate of the Florida Instructional League. On November 29, 1965, Closter was selected by the Cleveland Indians in the Rule 5 Draft. A few months later, on April 6, 1966, before ever playing a game in the Indians organization, Closter was purchased by the Washington Senators. Closter played only one game in the Senators organization, pitching 0.1 innings against the Baltimore Orioles in his MLB debut, before being purchased again by the Yankees on May 3, 1966. After returning to the New York Yankees organization, Closter finished the season with the Greensboro Yankees. Closter spent the entirety of the 1967 season with the double-ABinghamton Triplets of the Eastern League. Closter pitched in only 14 games that year, but made an impressive performance by going 40 with an ERA of 1.74 and 45 strikeouts. In 1968, Closter began the season with the single-A Fort Lauderdale Yankees of the Florida State League. Playing only five games there, he was quickly promoted to the triple-ASyracuse Chiefs of the International League. For the rest of his career with the Yankees, Closter would bounce between Syracuse and the Major Leagues. Between 1968 and 1973, Closter played a total of 249 games for Syracuse, winning a total of 69 games and losing a total of 58.
Major leagues
After making his Major League debut with the Senators in 1966, Closter wouldn't play another game in the MLB until 1971, when he made occasional relief appearances for the Yankees. Closter made one start in 1971 against the Detroit Tigers on September 4. He pitched 5.0 innings and allowed 5 hits and 5 earned runs, two of which were home runs. Closter was traded to the Atlanta Braves on September 5, 1973 as the player to be named later as part of a trade that sent Wayne Nordhagen and Frank Tepedino to Atlanta in exchange for pitcher Pat Dobson. In his remaining two seasons in the MLB, Closter only made 6 appearances between the Yankees and Braves, pitching 6.2 innings in relief.