Kempers became a professional tennis player in 1988. The first two years he played on the ATP Challenger Tour , initially without any major successes. In October 1990 he and his compatriot Richard Krajicek reached the final of the ATP tournament in Athens , which was lost. In 1991 he won his first double title with Jacco Eltingh in Palermo . In total, he celebrated four double titles on the ATP World Tour in the course of his career, plus seven more double titles on the ATP Challenger Tour. He reached his highest ranking in the tennis world rankings in 1994 with position 253 in singles and in 1998 with position 42 in doubles.
His best individual result in a Grand Slam tournament was reaching the first round of Wimbledon in 1996. There he was defeated by Brett Steven in three sets. This was also his only qualification for a Grand Slam tournament in singles. In the doubles competition, he reached the round of 16 of the Australian Open , the French Open and Wimbledon. In addition, he was twice in the mixed round of the US Open .