Glöckler began competing in the postwar German sports car scene in 1948, racing a Veritas RS in 1500 cc events at circuits including Hockenheim, the Grenzlandring, and the Sachsenring. In 1949 he dominated the German 1500 sports car championship in the Veritas, winning multiple rounds including at Hockenheim, Rund um Schotten, the Nürburgring Grand Prix, the Grenzlandring, and the Sachsenring, to claim the German 1500 sports car championship title.
After his Veritas period, Glöckler acquired a French DB sports car and fitted it with a BMW engine to compete in the German championship. In May 1951 at Hockenheim he gave the DB its only international victory, defeating the Emeryson of Ted Frost and the Cooper of Toni Kreuzer. He finished third overall in the 1951 West German Championship, and also entered the Eifelrennen at the Nürburgring that year in a DB for the Deutsch & Bonnet works team.
In 1952, Glöckler set a new class record at the Nürburgring driving the Glöckler-Porsche — the car his brother Walter had built — on his way to winning the German sports car championship. This was his second national championship title.
Glöckler became a Porsche works driver in 1953. At that year's Eifelrennen at the Nürburgring, run in heavy rain, he drove a prototype Porsche 550 to victory — giving the 550 its debut race win. That result confirmed both his standing as a trusted Porsche representative and the 550's potential as a serious competition machine.
Later in 1953 he co-drove a Porsche 550 Coupé with Hans Herrmann at the 24 Hours of Le Mans, the pair finishing 16th. He also entered the 1000 km Nürburgring in a Renault 4CV shared with Beckers, finishing 21st.
Glöckler entered the 1953 German Grand Prix under the banner of Equipe Anglaise in a Cooper T23 Formula Two car. Had he qualified and started, he would have raced under the number 0 — making him the first driver in Formula One World Championship history to carry that number, twenty years before Jody Scheckter used it at the 1973 Canadian Grand Prix. His engine failed during qualifying and he did not take the start.
Glöckler continued racing into 1954, 1955, and 1956. He won the German Sports Car Championship for the second time in 1954. At the 1954 Le Mans 24 Hours he co-drove a Porsche 550 with Richard von Frankenberg but retired. In the 1954 Mille Miglia he shared a Porsche 356 with Max Nathan, finishing 34th.
At the 1955 Mille Miglia he finished 8th overall with Wolfgang Seidel in a Porsche 550. That year's Le Mans saw him share a Porsche 550 with Jaroslav Juhan, the pair finishing 6th overall and 3rd in class. He also drove a Porsche 550 with Seidel at the 1955 Tourist Trophy, finishing 12th.
His last Le Mans appearance, in 1956, ended with an accident while co-driving a works Porsche 356 Carrera with Max Nathan.
Glöckler's brother Walter was responsible for creating the small hand-built Porsche-powered spyder in 1951 that inspired Porsche to develop the factory 550 — the very car Helm would go on to race as a works driver.