A tennis player was an athlete, a player in the sport of tennis.
After Doctor Julian Bashir was telepathically attacked and placed into a coma, by the Altovar, the Lethean revealed that he knew all about his victim. Altovar demonstrated this fact by revealing "When you were younger, you wanted to be a tennis player, didn't you." Bashir attempted to deny it by explaining that "I wasn't good enough to play professionally," however Altovar knew otherwise, stating, "Don't lie to me. Not in here. You were good enough. But you knew your parents [Richard and Amsha] wouldn't approve of it. So you gave up and you became a doctor instead."
As their interaction came to a head, Bashir later admitted that "As far as my career is concerned, I may have been a good tennis player, but I'm a great doctor." (DS9: "Distant Voices")