A coach was the individual responsible for coordinating and training a sports team.
Boothby described Nicholas Locarno's role as leader of Nova Squadron as "coach, surrogate father, and best friend". (TNG: "The First Duty")
In 2370, Jadzia Dax offered to set Arjin up with Trajok, saying that he was a great (wrestling) coach. (DS9: "Playing God")
In 2371, Miles O'Brien referred to Julian Bashir as coach after the doctor encouraged him during his darts match with Syvar. (DS9: "Shakaar")
In 2373, The Doctor's holographic daughter Belle worried that Coach Morgan would be furious with her if she was late for Parrises squares practice. (VOY: "Real Life")
In 2374, O'Brien offered to coach Bashir in tongo, believing they could beat Quark with a combination of Bashir's math skills and O'Brien's knowledge of strategy. (DS9: "Change of Heart")
In 2375, following O'Brien's injury of his clavicular joint and rotator cuff, he could no longer play third base. Instead, Benjamin Sisko made him batting, pitching, and first base coach. (DS9: "Take Me Out to the Holosuite")
B'Elanna Torres was part of the decathlon team of Starfleet Academy. When she left the academy, the track and field coach was furious with her. (VOY: "Basics, Part I")